A342675 - OEIS

%I #16 Mar 22 2021 14:59:45

%S 1,3,4,13,6,120,8,1161,2197,16148,12,603190,14,5773008,50422464,

%T 201359377,18,16590656229,20,269768284118,4748723771432,3138430473896,

%U 24,2972582195034162,476837158203151,3937376419253748,1350852564961601560,4066515044181860654,30,1036488835382356683530,32

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

%H Seiichi Manyama, <a href="/A342675/b342675.txt">Table of n, a(n) for n = 1..599</a>

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

%F If p is prime, a(p) = 1 + p.

%t a[n_] := DivisorSum[n, #^(n - # + 1) &]; Array[a, 30] (* _Amiram Eldar_, Mar 18 2021 *)

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

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

%Y Cf. A023887, A294645, A342628, A342677.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 18 2021