A359442 - OEIS

%I #50 Aug 09 2023 00:53:37

%S 1,2,2,4,2,15,2,74,83,643,2,12635,2,117715,397188,2359426,2,103572204,

%T 2,1260918355,13841818644,25937425627,2,5612318393211,152587890627,

%U 23298085126579,1853020231898564,2422197090649523,2,1032944452284531101,2,10376297939508166658

%N a(n) = Sum_{d|n} d^(n + 1 - d - n/d).

%H Seiichi Manyama, <a href="/A359442/b359442.txt">Table of n, a(n) for n = 1..605</a>

%F G.f.: Sum_{k>0} x^k / (1 - (k * x)^k / k).

%F If p is prime, a(p) = 2.

%t a[n_] := DivisorSum[n, #^(n + 1 - # - n/#) &]; Array[a, 32] (* _Amiram Eldar_, Aug 09 2023 *)

%o (PARI) a(n) = sumdiv(n, d, d^(n+1-d-n/d));

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k/k)))

%Y Cf. A294645, A342628, A342629, A342677, A359700.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 14 2023