A185302 a(n) = Sum_{d|n} d*sigma(n/d)^d.

1, 5, 7, 29, 11, 131, 15, 445, 214, 1315, 23, 6755, 27, 15475, 5807, 62589, 35, 207302, 39, 680419, 116277, 1948963, 47, 7702195, 38936, 20726659, 2365954, 72743987, 59, 227262211, 63, 735070461, 46142609, 2195383507, 2123475, 7556177030, 75, 22082968771

Offset

1,2

Comments

Logarithmic derivative of A185301.

Links

Table of n, a(n) for n=1..38.

Formula

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

Example

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 + ...

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A185301.

Sequence in context: A317166 A126888 A358582 * A179305 A307100 A229337

Adjacent sequences: A185299 A185300 A185301 * A185303 A185304 A185305

Keyword

nonn

Author

Paul D. Hanna, Jan 25 2012

Status

approved