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

0,2

Links

Table of n, a(n) for n=0..30.

Formula

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

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}]

Crossrefs

Cf. A005380, A030009, A030012, A065091.

Sequence in context: A120844 A110958 A141211 * A321645 A296315 A125671

Adjacent sequences: A353062 A353063 A353064 * A353066 A353067 A353068

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 21 2022

Status

approved