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

1,2

Links

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

Formula

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

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 *)

Prog

(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(#A<n, i++; if(is(i), listput(A, i))); Vec(A)}
seq(n)={my(A=MkS(n), p=1/prod(i=1, #A, 1 - x^A[i] + O(x*x^A[#A]))); vector(#A, i, polcoef(p, A[i]))} \\ Andrew Howroyd, Jan 02 2020

Crossrefs

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

Sequence in context: A018163 A339293 A195507 * A199594 A081172 A318301

Adjacent sequences: A117219 A117220 A117221 * A117223 A117224 A117225

Keyword

nonn

Author

Reinhard Zumkeller, Mar 04 2006

Extensions

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

Status

approved