A382513 - OEIS

%I #4 Apr 04 2025 22:44:56

%S 0,2,3,4,5,17,7,16,27,57,11,145,13,177,368,256,17,1241,19,1649,2530,

%T 2169,23,10657,3125,8361,19683,18785,29,107442,31,65536,178478,131361,

%U 94932,793585,37,524649,1596520,1439201,41,6997770,43,4208945,16302032

%N Expansion of Sum_{p prime} p * x^p / (1 - p * x^p).

%F a(n) = Sum_{p|n, p prime} p^(n/p).

%t nmax = 45; CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 - Prime[k] x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A008472, A055225, A069359, A373458, A373459.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Mar 30 2025