A308272 G.f. A(x) satisfies: A(x) = (1 + x) * A(x^2)*A(x^3)*A(x^5)* ... *A(x^prime(k))* ...

1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 13, 16, 22, 27, 33, 44, 53, 65, 84, 101, 124, 156, 187, 226, 280, 336, 403, 492, 587, 700, 850, 1008, 1195, 1435, 1693, 2004, 2390, 2808, 3303, 3910, 4584, 5372, 6328, 7387, 8619, 10106, 11757, 13675, 15961, 18508, 21464, 24948, 28845, 33345

Offset: 0

Author

Ilya Gutkovskiy, May 17 2019

Keywords

• nonn

Comments

Weigh transform of A008480.

Crossrefs

Cf. A000040, A008480, A129373, A308271.

Programs

Maple

g:= proc(n) option remember; (l-> add(i, i=l)!/
      mul(i!, i=l))(map(i-> i[2], ifactors(n)[2]))
    end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(g(i), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);  # Alois P. Heinz, May 17 2019

Mathematica

terms = 53; A[] = 1; Do[A[x] = (1 + x) Product[A[x^Prime[k]], {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

Formula

G.f.: Product_{k>=1} (1 + x^k)^A008480(k).