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%I #19 Dec 14 2024 12:24:34
%S 0,1,9,99,1301,20581,376891,7914216,186905206,4915451602,142368695176,
%T 4506118905870,154720069309364,5729167232515112,227585086051159866,
%U 9654819212943764500,435659280972794395356,20836049921760968809231,1052864549462731148832219
%N a(n) = Sum_{k=1..n} (k - 1)^n * floor(n/k).
%F a(n) = A319194(n) - A332469(n).
%F a(n) = Sum_{k=1..n} Sum_{d|k} (d - 1)^n.
%F a(n) = [x^n] (1/(1-x)) * Sum_{k>=1} (k - 1)^n * x^k/(1 - x^k).
%t Table[Sum[(k-1)^n Floor[n/k],{k,n}],{n,20}] (* _Harvey P. Dale_, Dec 14 2024 *)
%o (PARI) a(n) = sum(k=1, n, (k-1)^n*(n\k));
%o (PARI) a(n) = sum(k=1, n, sigma(k, n)-(n\k)^n);
%o (PARI) a(n) = sum(k=1, n, sumdiv(k, d, (d-1)^n));
%o (Python)
%o def A356100(n): return sum((k-1)**n*(n//k) for k in range(2,n+1)) # _Chai Wah Wu_, Jul 26 2022
%Y Cf. A121706, A236632, A319194, A332469.
%K nonn,changed
%O 1,3
%A _Seiichi Manyama_, Jul 26 2022