### Smarandache k-factorial

Let n and k be positive integers, with 1 =<
k =<
n-1.

As a generalization of the factorial and double factorial one defines the
Smarandache k-factorial of n as the below product of all possible strictly
positive factors:

SKF(n) = n(n-k)(n-2k)… .

Particular Cases:

S1F(n) is just the well-known factorial of n, i.e. n! = n(n-1)(n-2)…1

S2F(n) is just the well-known double factorial of n, i.e. n!! = n(n-2)(n-4)…
.

S3F(n) is the triple factorial of n, i.e. n!!! = n(n-3)(n-6)…
.

S4F(n) is the fourth factorial of n, i.e. S4F(n) = n(n-4)(n-8)…
.

Examples:

S3F(7) = 7(7-3)(7-6)
= 28.

S4F(8
) = 8(8-4)=32.

S10F(27)
= 27(27-10)(27-20)
= 27(17)7
= 3213.

Remark:

Many
Smarandache type functions, such as the Smarandache (classical) function, double
factorial function, ceil functions, etc. can be extended/transformed to this
k-factorial
definition.