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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..386
Programs
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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));
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PARI
a(n) = sum(k=1, n, sumdiv(k, d, sigma(d, d)));
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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