%I #22 Sep 08 2024 14:51:43
%S 1,7,36,315,3442,50926,874471,17717759,405157961,10414927743,
%T 295726598356,9214021189459,312089127781714,11424774177252514,
%U 449318695090042077,18896344248088180470,846136606134424944649,40192694877626991357901
%N a(n) = Sum_{k=1..n} sigma_k(k) * floor(n/k).
%H Seiichi Manyama, <a href="/A356076/b356076.txt">Table of n, a(n) for n = 1..386</a>
%F a(n) = Sum_{k=1..n} Sum_{d|k} sigma_d(d).
%F G.f.: (1/(1-x)) * Sum_{k>=1} sigma_k(k) * x^k/(1 - x^k).
%F a(n) ~ n^n. - _Vaclav Kotesovec_, Aug 07 2022
%t Table[Sum[DivisorSigma[k,k]Floor[n/k],{k,n}],{n,20}] (* _Harvey P. Dale_, Sep 08 2024 *)
%o (PARI) a(n) = sum(k=1, n, sigma(k, k)*(n\k));
%o (PARI) a(n) = sum(k=1, n, sumdiv(k, d, sigma(d, d)));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k, k)*x^k/(1-x^k))/(1-x))
%o (Python)
%o from sympy import divisor_sigma
%o 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
%Y Partial sums of A344434.
%Y Cf. A023887, A356046.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jul 25 2022