Smarandache Type Functions

 

BOOKS

Charles Ashbacher: An introduction to the Smarandache Function. Vail: Erhus University Press, 1995, 62 p.

C. Dumitrescu, V. Seleacu: The Smarandache Function. Vail: Erhus University Press, 1996, 136 p.

Sebastian Martin Ruiz: Aplicaciones de la Función de Smarandache y las Funciones Prima y Coprima. Rehoboth: American Research Press, 2002, 26 p.

Sebastian Martin Ruiz: Applications of Smarandache Function, and Prime and Coprime Functions. Rehoboth: American Research Press, 2002, 26 p.

Felice Russo: A Set of New Smarandache Functions, Sequences and Conjectures in Number Theory. Lupton: American Research Press, 2000, 108 p.

Marius Coman: Conjectures on Primes and Fermat Pseudoprimes, Many Based on Smarandache Function (Collected Papers). Columbus: Education Publishing, 2014, 84 p.

Charles Ashbacher: Pluckings from the Tree of Smarandache Sequences and Functions. Hiawatha: American Research Press, 1998, 90 p.

Eric W. Weisstein, CRC Encyclopedia of Mathematics, CRC Press, Boca Raton, FL, USA, WolframMathWorld:

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Smarandache Function, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/SmarandacheFunction.html

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Smarandache Ceil Function, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/SmarandacheCeilFunction.html

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Smarandache Kurepa Function, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/Smarandache-KurepaFunction.html

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Smarandache Wagstaff Function, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/Smarandache-WagstaffFunction.html

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Smarandache Near-to-Primordial Function, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/SmarandacheNear-to-PrimorialFunction.html

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Pseudo-Smarandache Function, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/PseudosmarandacheFunction.html

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Smarandache Number, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/SmarandacheNumber.html

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Smarandache-Wellin Number, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/Smarandache-WellinNumber.html

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Smarandache Prime, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/SmarandachePrime.html

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Smarandache-Wellin Prime, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/Smarandache-WellinPrime.html

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Smarandache Constants, CRC Encyclopedia of Mathematics, http://mathworld.wolfram.com/SmarandacheConstants.html

 

ARTICLES

Constantin Dumitrescu. (2010). A Brief History of the "Smarandache Function". 8 p. http://doi.org/10.5281/zenodo.852726.

MaohuaLe. (1998). A Formula of the Smarandache Function. 2 p. http://doi.org/10.5281/zenodo.852732.

Hailong Li. (2008). A generalization of the Smarandache function. In Scientia Magna, Vol. 4 (2008), No. 1, pp. 31-34. http://doi.org/10.5281/zenodo.852736

M. Andrei, I. Balacenoiu, C. Dumitrescu, E. Radescu, & V. Seleacu. (1995). A Linear Combination with Smarandache Function to Obtain the Identity. In Proceedings of Conference of 26th Annual Iranian Math. Conference, 28-31 March 1995, 5 p. http://doi.org/10.5281/zenodo.852754

Henry Ibstedt. (1995). Alternating Iterations of the sum of divisors Functions and the Pseudo-Smarandache Function. In Recreational Mathematics, 13 p. http://doi.org/10.5281/zenodo.852904

Yanchun Guo. (2005). A new additive function and the F. Smarandache function. In Scientia Magna, Vol. 5 (2009), No. 1, pp.128-132. http://doi.org/10.5281/zenodo.852944

Mihaly Bencze. (1997). A New Inequality for the Smarandache Function. 1 p. http://doi.org/10.5281/zenodo.852948

Jing Fu, & Yu Wang. (2008). A new Smarandache function and its elementary properties. In Scientia Magna, Vol. 4 (2008), No. 3, pp. 26-28. http://doi.org/10.5281/zenodo.852950

Henry Ibstedt. (1997). An Illustration of the Distribution of the Smarandache Function. 2 p. http://doi.org/10.5281/zenodo.852952

Maohua Le. (1995). An Inequality Concerning the Smarandache Function. 2 p. http://doi.org/10.5281/zenodo.852954

Weiyi Zhu. (2008). An inequality of the Smarandache function. In Scientia Magna, Vol. 4 (2008), No. 1, pp. 130-133. http://doi.org/10.5281/zenodo.852956

Marius Coman. (1997). An ordered set of certain seven numbers that results constantly from a recurrence formula based on Smarandache function. 2 p. http://doi.org/10.5281/zenodo.852958

A.A.K. Majumdar. (2008). A note on the near pseudo Smarandache function. In Scientia Magna, Vol. 4 (2008), No. 4, pp. 104-111. http://doi.org/10.5281/zenodo.852960

Marius Coman. A recurrent formula inspired by Rowland’s formula and based on Smarandache function which might be a criterion for primality, 200, 2 p. http://doi.org/10.5281/zenodo.852962

Sebastian Martin Ruiz. (1998). A result obtained using Smarandache Function. 2 p. http://doi.org/10.5281/zenodo.852964

Henry Ibstedt. (1995). Base Solution (the Smarandache Function). 4 p. http://doi.org/10.5281/zenodo.852966

Mark Farris & Patrick Mitchell. (1997). Bounding the Smarandache Function. 6 pages. http://doi.org/10.5281/zenodo.852972

Sabin Tabirca, Tatiana Tabirca, Kieran Reynolds, & Laurence T Yang. (2004). Calculating Smarandache Function in Parallel. 4 pages. http://doi.org/10.5281/zenodo.852974

J. R. Sutton. (1995). Calculating the Smarandache Function for Powers of a Prime. 3 pages. http://doi.org/10.5281/zenodo.852976

Marius Coman. (2001). Five conjectures on Sophie Germain primes and Smarandache function and the notion of Smarandache-Germain primes. 3 pages. Zenodo. http://doi.org/10.5281/zenodo.852978

Balacenoiu I. & V. Seleacu. (1994). History of The Smarandache Function. 10 pages. http://doi.org/10.5281/zenodo.852990

Yi Yuan, & Zhang Wenpeng. (2013). Mean Value of The Additive Analogue of Smarandache Function. In Scientia Magna Vol. 1, No. 1, pp. 145-147. http://doi.org/10.5281/zenodo.852992

Zhu Minhui. (2013). Mean Value of The Additive Analogue of Smarandache Function. In Scientia Magna Vol. 1, No. 1, pp. 149-182. http://doi.org/10.5281/zenodo.852996

Steven R Finch. (1997). Moments of The Smarandache Function. 2 p. http://doi.org/10.5281/zenodo.852998

A.W. Vyawahare, & K. M. Purohit. (1997). Near Pseudo Smarandache Function. 20 pages.  http://doi.org/10.5281/zenodo.853000

Jozsef Sandor. (1995). On a dual of the Pseudo-Smarandache function. 6 pages. http://doi.org/10.5281/zenodo.853002

J. Sandor. (1995). On an inequality for the Smarandache function. 3 pages. http://doi.org/10.5281/zenodo.853006

J. Sandor. (1997). On certain generalizations of the Smarandache function. 11 pages. http://doi.org/10.5281/zenodo.853010

Sandor Jozsef. (1997). On Certain Inequalities Involving the Smarandache Function. 4 pages. http://doi.org/10.5281/zenodo.853012

Jozsef Sandor. (1995). On certain new inequalities and limits for the Smarandache function. 8 pages. http://doi.org/10.5281/zenodo.853016

Wei Qin. (2008). One problem related to the Smarandache function. In Scientia Magna, Vol. 4 (2008), No. 3, pp. 106-108. http://doi.org/10.5281/zenodo.853018

Charles Ashbacher. (2000). On Numbers where the Values of the Pseudo-Smarandache Function of It and The Reversal Are Identical. 3 pages. http://doi.org/10.5281/zenodo.853022

A.A.K. Majumdar. (2008). On some pseudo Smarandache function related triangles. In Scientia Magna, Vol. 4 (2008), No. 3, pp. 95-105. http://doi.org/10.5281/zenodo.853024

Emil Burton. (2002). On Some Series Involving Smarandache Function. 3 pages. http://doi.org/10.5281/zenodo.853030

C. Dumitrescu, & C. Rocsoreanu. (1995). On the Calculus of Smarandache Function. 8 pages. http://doi.org/10.5281/zenodo.853034

Zhongtian Lv. (2007). On the F.Smarandache function and its mean value. In Scientia Magna, Vol. 3 (2007), No. 2, pp. 104-108. http://doi.org/10.5281/zenodo.853036

Chan Shi. (2010). On the hybrid mean value of the Smarandache kn-digital sequence and Smarandache function. In Scientia Magna, Vol. 6 (2010), No. 4, pp. 20-23. http://doi.org/10.5281/zenodo.853038

J. Sandor. (2011). On the Irrationality of Certain Constants Related to the Smarandache Function. 3 pages. http://doi.org/10.5281/zenodo.853040

Lin Cheng. (2007). On the mean value of the Pseudo-Smarandache function. In Scientia Magna, Vol. 3 (2007), No. 3, pp. 97-100. http://doi.org/10.5281/zenodo.853042

Hai Yang, & Ruiqin Fu. (2006). On the mean value of the Near Pseudo Smarandache Function. In Scientia Magna, Vol. 2 (2006), No. 2, pp. 35-39.  http://doi.org/10.5281/zenodo.853044

Yongfeng Zhang. (2007). On the near pseudo Smarandache function. In Scientia Magna, Vol. 3 (2007), No. 1, pp. 98-101. http://doi.org/10.5281/zenodo.853048

Xuhui Fan. (2008). On the Pseudo-Smarandache-Squarefree function and Smarandache function. In Scientia Magna, Vol. 4 (2008), No. 4, pp. 7-11. http://doi.org/10.5281/zenodo.853050

J. Sandor. (1997). On the Pseudo-Smarandache Function. 3 pages. http://doi.org/10.5281/zenodo.853056

Yani Zheng. (2007). On the Pseudo Smarandache function and its two conjectures. In Scientia Magna, Vol. 3 (2007), No. 4, pp. 74-76. http://doi.org/10.5281/zenodo.853058

Henry Ibstedt. (2011). On the Pseudo-Smarandache Function and Iteration Problems Part II: The Sum of Divisors Function. 5 pages. http://doi.org/10.5281/zenodo.853062

Yuanbing Lou. (2007). On the pseudo Smarandache function. In Scientia Magna, Vol. 3 (2007), No. 4, pp. 48-50. http://doi.org/10.5281/zenodo.853064

Su Gou, & Jianghua Li. (2007). On the Pseudo-Smarandache function. In Scientia Magna, Vol. 3 (2007), No. 4, pp. 81-83. http://doi.org/10.5281/zenodo.853068

Henry Ibstedt. (2011). On the Pseudo-Smarandache Function and Iteration Problems. 8 pages. http://doi.org/10.5281/zenodo.853074

Mingdong Xiao. (2008). On the Smarandache function and the divisor product sequences. In Scientia Magna, Vol. 5 (2009), No. 2, pp. 129-132. http://doi.org/10.5281/zenodo.853076

Jinrui Wang. (2008). On the Smarandache function and the Fermat number. In Scientia Magna, Vol. 4 (2008), No. 2, pp. 25-28. http://doi.org/10.5281/zenodo.853078

Albert A. Mullin. (2000). On the Smarandache Function and The Fixed - Point Theory of Numbers. 1 page. http://doi.org/10.5281/zenodo.853080

Zhang Wenpeng, & Xu Zhefeng. (2004). On the Smarandache Function and Square Complements. In Scientia Magna Vol. 1, No. 1, 3 pages. http://doi.org/10.5281/zenodo.853082

Lu Yaming. (2006). On the solutions of an equation involving the Smarandache function. In Scientia Magna, Vol. 2 (2006), No. 1, pp. 76-79. http://doi.org/10.5281/zenodo.853084

Weiguo Duany, & Yanrong Xue. (2008). On the solvability of an equation involving the Smarandache function and Euler function. In Scientia Magna, Vol. 4 (2008), No. 2, pp. 29-33. http://doi.org/10.5281/zenodo.853086

Mihaly Bencze. (2011). Open Questions for The Smarandache Function. 3 pages. http://doi.org/10.5281/zenodo.853088

Charles Ashbacher. (2011). Palindromic Numbers and Iterations of the Pseudo-Smarandache Function. 2 pages. http://doi.org/10.5281/zenodo.853090

A.S. Muktibodh, & S.T. Rathod. (2011). Pseudo-Smarandache Functions of First and Second Kind. In International J.Math. Combin. Vol. 3, (2011), pp. 17-22 http://doi.org/10.5281/zenodo.853094

Ion Balacenoiu, & Constantin Dumitrescu. (2011). Smarandache Functions of The Second Kind. 4 pages. http://doi.org/10.5281/zenodo.853096

H. Ibstedt. (1993). The Smarandache function S(n). 2 p.  http://doi.org/10.5281/zenodo.853516

Zhong Li. (2004). Solution of Two Questions Concerning the Divisor Function And The Pseudo-Smarandache Function. 4 p.  http://doi.org/10.5281/zenodo.853518

Constantin Dumitrescu, & Cannen Rocsoreanu. (2002). Some Connections Between the Smarandache Function and the Fibonacci Sequence. 11 p.  http://doi.org/10.5281/zenodo.853522

E. Burton, L. Cojocaru, S. Cojocaru, & C. Dumitrescu. (1994). 8 pages. Some Convergence Problems Involving the Smarandache Function. http://doi.org/10.5281/zenodo.853526

I. Radescu, N. Radescu, & C. Dumitrescu. (1992). Some Elementary Algebraic Considerations Inspired by The Smarandache Function. 5 pages. http://doi.org/10.5281/zenodo.853534

Yu Wang. (2007). Some identities involving the near pseudo Smarandache function. In Scientia Magna, Vol. 3 (2007), No. 2, pp. 44-49. http://doi.org/10.5281/zenodo.853540

Kang Xiaoyu. (2005). Some interesting properties of the Smarandache function. In Scientia Magna, Vol. 1 (2005), No. 2, pp. 52-54. http://doi.org/10.5281/zenodo.853596

Yulin Lu. (2007). Some new problems about the Smarandache function and related problems. In Scientia Magna, Vol. 3 (2007), No. 3, pp. 110-111. http://doi.org/10.5281/zenodo.853654

Richard Pinch. (2005). Some properties of the Pseudo-Smarandache function. In Scientia Magna, Vol. 1 (2005), No. 2, pp. 167-172. http://doi.org/10.5281/zenodo.853702

Balacenoiu I. & V. Seleacu. (1990). Some Properties of Smarandache Functions of The Type I. 5 pages. http://doi.org/10.5281/zenodo.853754

Richard Pinch. (2005). Some Properties of The Pseudo-Smarandache Function. In arXiv:math/0504118v1 [math.NT] 6 Apr 2005. http://doi.org/10.5281/zenodo.853758

Tomita Tiberiu Florin. (1997). Some Remarks Concerning the Distribution of The Smarandache Function.  6 pages. http://doi.org/10.5281/zenodo.853774

M. Andrei, C. Dumitrescu, V. Seleacu, L. Tutescu, & St. Zamfir. (1997). Some Remarks on the Smarandache Function. 5 pages. http://doi.org/10.5281/zenodo.853834

Florian Luca. (1997). The Average Smarandache Function. 9 pages. http://doi.org/10.5281/zenodo.854294

Steven R. Finch. (2007). The Average Value of The Smarandache Function. 2 pages. http://doi.org/10.5281/zenodo.854298

Dhananjay P. Mehendale. (2007). The Classical Smarandache Function and a Formula for Twin Primes. 3 pages. http://doi.org/10.5281/zenodo.854306

Henry Ibstedt. (1993). The Florentin Smarandache Function S(n). 4 pages. http://doi.org/10.5281/zenodo.854308

Baohuai Shi. (2006). The hybrid mean value of the Smarandache function and the Mangoldt function. In Scientia Magna, Vol. 2 (2006), No. 4, pp. 98-100. http://doi.org/10.5281/zenodo.854310

Ion Balacenoiu. (1997). The Monotony of Smarandache Functions of First Kind. 7 pages. http://doi.org/10.5281/zenodo.854312

Kevin Ford. (2007). The Normal Behavior of the Smarandache Function. 6 pages. http://doi.org/10.5281/zenodo.854316

David Gorski. (2007). The Pseudo-Smarandache Function. 10 pages. http://doi.org/10.5281/zenodo.854322

Charles Ashbacher. (2007). The Pseudo-Smarandache Function and the Classical Functions of Number Theory.4 pages. http://doi.org/10.5281/zenodo.854326

Pal Gronas. (1992). The Solution of the Diophantine Equation. 3 pages. http://doi.org/10.5281/zenodo.854332

Charles Ashbacher. (2016). PalindromicNumbers of Pseudo-Smarandache Function. 5 pages. http://doi.org/10.5281/zenodo.854334

Wenpeng Zhang, & Ling Li. (2008). Two problems related to the Smarandache function. In Scientia Magna, Vol. 4 (2008), No. 2, pp.1-3. http://doi.org/10.5281/zenodo.854342

 

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