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A353078
Inverse Moebius transform of odd primes.
1
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
1,1
FORMULA
G.f.: Sum_{k>=1} prime(k+1) * x^k / (1 - x^k).
a(n) = Sum_{d|n} prime(d+1).
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}]
PROG
(PARI) a(n) =sumdiv(n, d, prime(d+1)); \\ Michel Marcus, Apr 22 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 22 2022
STATUS
approved