

Smarandache kfactorial
Let n and k be positive integers, with 1 =< k =< n1. As a generalization of the factorial and double factorial one defines the Smarandache kfactorial of n as the below product of all possible strictly positive factors: SKF(n) = n(nk)(n2k)… . Particular Cases: S1F(n) is just the wellknown factorial of n, i.e. n! = n(n1)(n2)…1 S2F(n) is just the wellknown double factorial of n, i.e. n!! = n(n2)(n4)… . S3F(n) is the triple factorial of n, i.e. n!!! = n(n3)(n6)… . S4F(n) is the fourth factorial of n, i.e. S4F(n) = n(n4)(n8)… . Examples: S3F(7) = 7(73)(76) = 28. S4F(8
) = 8(84)=32. S10F(27) = 27(2710)(2720) = 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
kfactorial 