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%I #9 Apr 26 2022 11:53:05
%S 3,8,10,19,16,32,22,42,39,52,40,84,46,74,76,101,64,128,74,136,108,128,
%T 92,204,117,154,146,194,116,256,134,238,186,218,186,337,166,246,226,
%U 338,184,368,196,336,304,308,226,490,251,386,310,406,254,492,316,486,352,398,284,664
%N Inverse Moebius transform of odd primes.
%F G.f.: Sum_{k>=1} prime(k+1) * x^k / (1 - x^k).
%F a(n) = Sum_{d|n} prime(d+1).
%t nmax = 60; CoefficientList[Series[Sum[Prime[k + 1] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t Table[DivisorSum[n, Prime[# + 1] &], {n, 1, 60}]
%o (PARI) a(n) =sumdiv(n, d, prime(d+1)); \\ _Michel Marcus_, Apr 22 2022
%Y Cf. A007445, A030014, A065091.
%K nonn
%O 1,1
%A _Ilya Gutkovskiy_, Apr 22 2022