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

%I A356076 #22 Sep 08 2024 14:51:43
%S A356076 1,7,36,315,3442,50926,874471,17717759,405157961,10414927743,
%T A356076 295726598356,9214021189459,312089127781714,11424774177252514,
%U A356076 449318695090042077,18896344248088180470,846136606134424944649,40192694877626991357901
%N A356076 a(n) = Sum_{k=1..n} sigma_k(k) * floor(n/k).
%H A356076 Seiichi Manyama, <a href="/A356076/b356076.txt">Table of n, a(n) for n = 1..386</a>
%F A356076 a(n) = Sum_{k=1..n} Sum_{d|k} sigma_d(d).
%F A356076 G.f.: (1/(1-x)) * Sum_{k>=1} sigma_k(k) * x^k/(1 - x^k).
%F A356076 a(n) ~ n^n. - _Vaclav Kotesovec_, Aug 07 2022
%t A356076 Table[Sum[DivisorSigma[k,k]Floor[n/k],{k,n}],{n,20}] (* _Harvey P. Dale_, Sep 08 2024 *)
%o A356076 (PARI) a(n) = sum(k=1, n, sigma(k, k)*(n\k));
%o A356076 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, sigma(d, d)));
%o A356076 (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 A356076 (Python)
%o A356076 from sympy import divisor_sigma
%o A356076 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 A356076 Partial sums of A344434.
%Y A356076 Cf. A023887, A356046.
%K A356076 nonn
%O A356076 1,2
%A A356076 _Seiichi Manyama_, Jul 25 2022