A359701 - OEIS

%I #16 Aug 14 2023 02:00:14

%S 1,3,10,69,626,7812,117650,2097425,43046803,1000003158,25937424602,

%T 743008418676,23298085122482,793714774077816,29192926025406980,

%U 1152921504623628545,48661191875666868482,2185911559739084235093,104127350297911241532842

%N a(n) = Sum_{d|n} d^(d + n/d - 2).

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

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

%t a[n_] := DivisorSum[n, #^(# + n/# - 2) &]; Array[a, 20] (* _Amiram Eldar_, Aug 14 2023 *)

%o (PARI) a(n) = sumdiv(n, d, d^(d+n/d-2));

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k-1)*x^k/(1-k*x^k)))

%Y Cf. A082245, A124923, A262843, A294956.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 11 2023