A309368 a(n) = Sum_{d|n} prime(n/d)^d.

2, 7, 13, 32, 43, 129, 145, 405, 660, 1417, 2079, 5999, 8233, 18903, 37271, 74912, 131131, 300239, 524355, 1139985, 2180263, 4372491, 8388691, 17853809, 33715580, 68704969, 136183123, 274127445, 536871021, 1100025921, 2147483775, 4343912079, 8638792645, 17309012967, 34380645545

Offset: 1

Author

Ilya Gutkovskiy, Jul 25 2019

Keywords

• nonn

Crossrefs

Cf. A000040, A007445, A055225.

Programs

Mathematica

Table[Sum[Prime[n/d]^d, {d, Divisors[n]}], {n, 1, 35}]
nmax = 35; CoefficientList[Series[Sum[Prime[k] x^k/(1 - Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
nmax = 35; CoefficientList[Series[-Log[Product[(1 - Prime[k] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest

Formula

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

L.g.f.: -log(Product_{k>=1} (1 - prime(k)*x^k)^(1/k)).

a(n) ~ 2^n.