A321141 a(n) = Sum_{d|n} sigma_n(d).

1, 6, 29, 291, 3127, 48246, 823545, 16909060, 387459858, 10019533302, 285311670613, 8920489178073, 302875106592255, 11113363271736486, 437893951444713443, 18447307036548136965, 827240261886336764179, 39346708467688595378892, 1978419655660313589123981

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

N. J. A. Sloane, Transforms

Formula

a(n) = [x^n] Sum_{k>=1} sigma_n(k)*x^k/(1 - x^k).

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

a(n) ~ n^n. - Vaclav Kotesovec, Feb 16 2020

Maple

with(numtheory): seq(coeff(series(add(sigma[n](k)*x^k/(1-x^k), k=1..n), x, n+1), x, n), n = 1 .. 20); # Muniru A Asiru, Oct 28 2018

Mathematica

Table[Sum[DivisorSigma[n, d], {d, Divisors[n]}] , {n, 19}]
Table[SeriesCoefficient[Sum[DivisorSigma[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 19}]

Prog

(PARI) a(n) = sumdiv(n, d, sigma(d, n)); \\ Michel Marcus, Oct 28 2018
(Python)
from sympy import divisor_sigma, divisors
def A321141(n):
    return sum(divisor_sigma(d, 0)*(n//d)**n for d in divisors(n, generator=True)) # Chai Wah Wu, Feb 15 2020
(Magma) [&+[DivisorSigma(n, d):d in Divisors(n)]:n in [1..20]]; // Vincenzo Librandi, Feb 16 2020

Crossrefs

Cf. A000005, A007429, A007433, A023887, A319194, A320940, A321140.

Sequence in context: A143563 A266205 A344434 * A359053 A122802 A144746

Adjacent sequences: A321138 A321139 A321140 * A321142 A321143 A321144

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 28 2018

Status

approved