A243758 a(n) = Product_{i=1..n} A234959(i).

1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 6, 6, 36, 36, 36, 36, 36, 36, 216, 216, 216, 216, 216, 216, 1296, 1296, 1296, 1296, 1296, 1296, 7776, 7776, 7776, 7776, 7776, 7776, 279936, 279936, 279936, 279936, 279936, 279936, 1679616, 1679616, 1679616, 1679616, 1679616, 1679616, 10077696

Offset: 0

Author

Tom Edgar, Jun 10 2014

Keywords

• nonn
• easy

Comments

This is the generalized factorial for A234959.

a(0) = 1 as it represents the empty product.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.

Crossrefs

Cf. A060828, A060818, A234959, A242954, A243757.

Programs

Haskell

a243758 n = a243758_list !! n
a243758_list = scanl (*) 1 a234959_list
-- Reinhard Zumkeller, Feb 09 2015

Mathematica

Table[Product[6^IntegerExponent[k, 6], {k, 1, n}], {n, 0, 20}] (* G. C. Greubel, Dec 24 2016 *)

PARI

valp(n,p)=my(s); while(n\=p, s+=n); s
a(n)=6^valp(n,6) \\ Charles R Greathouse IV, Oct 03 2016

Sage

S=[0]+[6^valuation(i,6) for i in [1..100]]
[prod(S[1:i+1]) for i in [0..99]]

Formula

a(n) = Product_{i=1..n} A234959(i).

a(n) = 6^(A054895(n)).