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%I #7 Sep 08 2022 08:46:25
%S 1,5,36,289,3433,47578,842499,16850338,389415029,10010878371,
%T 285679026506,8918295095267,302973286652448,11112691430262573,
%U 437929106387544254,18447028378472722051,827256956775203666857,39346558275376372606086,1978429667078835508142129
%N a(n) = Sum_{k=1..n} ceiling(n/k)^n.
%F a(n) = [x^n] x/(1 - x)^2 + (x/(1 - x)) * Sum_{k>=1} ((k + 1)^n - k^n) * x^k / (1 - x^k).
%F a(n) = n + Sum_{k=1..n-1} Sum_{d|k} ((d + 1)^n - d^n).
%t Table[Sum[Ceiling[n/k]^n, {k, 1, n}], {n, 1, 19}]
%t Table[n + Sum[Sum[(d + 1)^n - d^n, {d, Divisors[k]}], {k, 1, n - 1}], {n, 1, 19}]
%t Table[SeriesCoefficient[x/(1 - x)^2 + x/(1 - x) Sum[((k + 1)^n - k^n) x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 19}]
%o (Magma) [&+[Ceiling(n/k)^n:k in [1..n]]:n in [1..20]]; // _Marius A. Burtea_, Feb 17 2020
%Y Cf. A006590, A031971, A332469, A332490, A332623.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Feb 17 2020
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