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%I #23 Oct 27 2023 09:57:30
%S 1,5,29,274,3160,47452,825862,16843268,387702833,10009826727,
%T 285360679985,8918294547447,302888236005847,11112685321898449,
%U 437898668488710801,18447025705612363530,827242514466399305122,39346558271561286347116,1978421007121668206129316
%N a(n) = Sum_{k=1..n} floor(n/k)^n.
%H Seiichi Manyama, <a href="/A332469/b332469.txt">Table of n, a(n) for n = 1..386</a>
%F a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k / (1 - x^k).
%F a(n) ~ n^n. - _Vaclav Kotesovec_, Jun 11 2021
%t Table[Sum[Floor[n/k]^n, {k, 1, n}], {n, 1, 19}]
%t Table[SeriesCoefficient[1/(1 - x) Sum[(k^n - (k - 1)^n) x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 19}]
%o (PARI) a(n)={sum(k=1, n, floor(n/k)^n)} \\ _Andrew Howroyd_, Feb 13 2020
%o (Magma) [&+[Floor(n/k)^n:k in [1..n]]:n in [1..20]]; // _Marius A. Burtea_, Feb 13 2020
%o (Python)
%o from math import isqrt
%o def A332469(n): return -(s:=isqrt(n))**(n+1)+sum((q:=n//k)*(k**n-(k-1)**n+q**(n-1)) for k in range(1,s+1)) # _Chai Wah Wu_, Oct 26 2023
%Y Cf. A006218, A222548, A318742, A318743, A318744, A319194, A332468.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Feb 13 2020
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