A353065 Euler transform of odd primes.

1, 3, 11, 32, 92, 239, 608, 1465, 3450, 7858, 17525, 38165, 81653, 171497, 354785, 723084, 1454642, 2889854, 5676607, 11031046, 21224439, 40453596, 76428636, 143192339, 266172016, 491072611, 899583306, 1636775949, 2958900040, 5316004485, 9494514599

Offset: 0

Author

Ilya Gutkovskiy, Apr 21 2022

Keywords

• nonn

Crossrefs

Cf. A005380, A030009, A030012, A065091.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
      d*ithprime(d+1), d=numtheory[divisors](j)), j=1..n)/n)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 21 2022

Mathematica

nmax = 30; CoefficientList[Series[Product[1/(1 - x^k)^Prime[k + 1], {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Sum[d Prime[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]

Formula

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