A353078 Inverse Moebius transform of odd primes.

3, 8, 10, 19, 16, 32, 22, 42, 39, 52, 40, 84, 46, 74, 76, 101, 64, 128, 74, 136, 108, 128, 92, 204, 117, 154, 146, 194, 116, 256, 134, 238, 186, 218, 186, 337, 166, 246, 226, 338, 184, 368, 196, 336, 304, 308, 226, 490, 251, 386, 310, 406, 254, 492, 316, 486, 352, 398, 284, 664

Offset: 1

Author

Ilya Gutkovskiy, Apr 22 2022

Keywords

• nonn

Crossrefs

Cf. A007445, A030014, A065091.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[Prime[k + 1] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, Prime[# + 1] &], {n, 1, 60}]

PARI

a(n) =sumdiv(n, d, prime(d+1)); \\ Michel Marcus, Apr 22 2022

Formula

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

a(n) = Sum_{d|n} prime(d+1).