A356076 a(n) = Sum_{k=1..n} sigma_k(k) * floor(n/k).

1, 7, 36, 315, 3442, 50926, 874471, 17717759, 405157961, 10414927743, 295726598356, 9214021189459, 312089127781714, 11424774177252514, 449318695090042077, 18896344248088180470, 846136606134424944649, 40192694877626991357901

Offset: 1

Author

Seiichi Manyama, Jul 25 2022

Keywords

• nonn

Links

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

Crossrefs

Partial sums of A344434.

Cf. A023887, A356046.

Programs

Mathematica

Table[Sum[DivisorSigma[k,k]Floor[n/k],{k,n}],{n,20}] (* Harvey P. Dale, Sep 08 2024 *)

PARI

a(n) = sum(k=1, n, sigma(k, k)*(n\k));

PARI

a(n) = sum(k=1, n, sumdiv(k, d, sigma(d, d)));

PARI

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

Python

from sympy import divisor_sigma
def A356079(n): return n+sum(divisor_sigma(k,k)*(n//k) for k in range(2,n+1)) # Chai Wah Wu, Jul 25 2022

Formula

a(n) = Sum_{k=1..n} Sum_{d|k} sigma_d(d).

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

a(n) ~ n^n. - Vaclav Kotesovec, Aug 07 2022