A185302 - OEIS

%I #15 Aug 20 2023 10:50:50

%S 1,5,7,29,11,131,15,445,214,1315,23,6755,27,15475,5807,62589,35,

%T 207302,39,680419,116277,1948963,47,7702195,38936,20726659,2365954,

%U 72743987,59,227262211,63,735070461,46142609,2195383507,2123475,7556177030,75,22082968771

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

%C Logarithmic derivative of A185301.

%F L.g.f.: Sum_{n>=1} Sum_{k>=1} sigma(n)^k * x^(n*k)/n = Sum_{n>=1} a(n)*x^n/n.

%e L.g.f.: L(x) = x + 5*x^2/2 + 7*x^3/3 + 29*x^4/4 + 11*x^5/5 + 131*x^6/6 + ... where exp(L(x)) = 1 + x + 3*x^2 + 5*x^3 + 14*x^4 + 20*x^5 + 59*x^6 + 83*x^7 + 229*x^8 + 350*x^9 + 878*x^10 + ... + A185301(n)*x^n + ...

%t a[n_] := DivisorSum[n, # * DivisorSigma[1, n/#]^# &]; Array[a, 40] (* _Amiram Eldar_, Aug 18 2023 *)

%o (PARI) {a(n)=sumdiv(n,d,d*sigma(n/d)^d)}

%Y Cf. A000203, A185301.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jan 25 2012