A308271 G.f. A(x) satisfies: A(x) = (1/(1 - x)) * A(x^2)*A(x^3)*A(x^5)* ... *A(x^prime(k))* ...

1, 1, 2, 3, 5, 7, 12, 16, 24, 33, 48, 64, 93, 122, 169, 224, 303, 395, 532, 686, 907, 1168, 1523, 1943, 2521, 3193, 4094, 5170, 6573, 8245, 10434, 13015, 16344, 20321, 25363, 31379, 39003, 48039, 59384, 72914, 89720, 109722, 134528, 163929, 200149, 243199, 295831, 358280

Offset: 0

Author

Ilya Gutkovskiy, May 17 2019

Keywords

• nonn

Comments

Euler transform of A008480.

Crossrefs

Cf. A000040, A008480, A129374, A308272.

Programs

Maple

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

Mathematica

terms = 47; A[] = 1; Do[A[x] = 1/(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/(1 - x^k)^A008480(k).