A117222 Number of partitions of 3-smooth numbers into 3-smooth numbers.

1, 2, 3, 5, 10, 18, 23, 53, 128, 194, 586, 947, 2070, 3667, 16762, 33036, 93402, 200626, 445869, 1517300, 3715025, 14526494, 39369076, 111448616, 541299314, 1713653236, 5690596129, 9832997667, 35075665070, 131672592907, 973547058482, 4162255238584, 18810021557460

Offset: 1

Author

Reinhard Zumkeller, Mar 04 2006

Keywords

• nonn

Links

• David A. Corneth, Table of n, a(n) for n = 1..200 (first 100 terms from Andrew Howroyd)

Crossrefs

Cf. A003586, A090184, A105420, A117220, A117221.

Programs

Mathematica

is[n_] := n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3] == 1;
MkS[n_] := Module[{A = {}, i = 0}, While[Length[A] < n, i++; If[is[i], AppendTo[A, i]]]; A];
seq[n_] := Module[{A = MkS[n], p}, p = 1/Product[1 - x^A[[i]] + O[x]^(1 + A[[Length[A]]]), {i, Length[A]}] // Normal; Table[Coefficient[p, x, A[[i]]], {i, Length[A]}]];
seq[33] (* Jean-François Alcover, Oct 13 2021, after Andrew Howroyd *)

PARI

\\ here is(n) is test for A003586 inclusion.
is(n)={forprime(p=2, 3, n/=p^valuation(n,p)); n==1}
MkS(n)={my(A=List(), i=0); while(#AAndrew Howroyd, Jan 02 2020

Formula

a(n) = A105420(A003586(n)).

Extensions

Terms a(23) and beyond from Andrew Howroyd, Jan 02 2020