A309368 - OEIS

%I #5 Jul 25 2019 17:44:41

%S 2,7,13,32,43,129,145,405,660,1417,2079,5999,8233,18903,37271,74912,

%T 131131,300239,524355,1139985,2180263,4372491,8388691,17853809,

%U 33715580,68704969,136183123,274127445,536871021,1100025921,2147483775,4343912079,8638792645,17309012967,34380645545

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

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

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

%F a(n) ~ 2^n.

%t Table[Sum[Prime[n/d]^d, {d, Divisors[n]}], {n, 1, 35}]

%t nmax = 35; CoefficientList[Series[Sum[Prime[k] x^k/(1 - Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%t nmax = 35; CoefficientList[Series[-Log[Product[(1 - Prime[k] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest

%Y Cf. A000040, A007445, A055225.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Jul 25 2019