A356238
a(n) = Sum_{k=1..n} (k * floor(n/k))^n.
Original entry on oeis.org
1, 8, 62, 849, 8541, 206345, 2581403, 76623522, 1617299079, 49463993875, 952905453423, 59000021366675, 1198427462876421, 54128102218676115, 2321105129608323165, 117387839988330848902, 3205342976298888473968, 268263812478494295219717
Offset: 1
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a[n_] := Sum[(k * Floor[n/k])^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 30 2022 *)
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a(n) = sum(k=1, n, (k*(n\k))^n);
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a(n) = sum(k=1, n, k^n*sumdiv(k, d, 1-(1-1/d)^n));
A356243
a(n) = Sum_{k=1..n} k^2 * sigma_{n-2}(k).
Original entry on oeis.org
1, 9, 49, 447, 4607, 71009, 1210855, 24980627, 575624572, 14958422046, 427890493960, 13431874937840, 457651929853662, 16844143705998554, 665499756005678382, 28102799297908820326, 1262909308355648335240, 60183118566605371095996
Offset: 1
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a[n_] := Sum[k^2 * DivisorSigma[n - 2, k], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 30 2022 *)
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a(n) = sum(k=1, n, k^2*sigma(k, n-2));
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a(n) = sum(k=1, n, k^n*sum(j=1, n\k, j^2));
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from math import isqrt
from sympy import bernoulli
def A356243(n): return (((s:=isqrt(n))*(s+1)*(2*s+1))*((b:=bernoulli(n+1))-bernoulli(n+1, s+1)) + sum(k**n*(n+1)*((q:=n//k)*(q+1)*(2*q+1))+6*k**2*(bernoulli(n+1,q+1)-b) for k in range(1,s+1)))//(n+1)//6 # Chai Wah Wu, Oct 21 2023
A356240
a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^n.
Original entry on oeis.org
0, 1, 9, 114, 1332, 25404, 395460, 9724901, 207584371, 6120938951, 151737244257, 5932533980409, 168400694345669, 7145593797561899, 260681076993636793, 12410128414690753548, 473029927456547840472, 27572016889372245275679
Offset: 1
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a[n_] := Sum[(k - 1)^n * Sum[j^n, {j, 1, Floor[n/k]}], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 30 2022 *)
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a(n) = sum(k=1, n, (k-1)^n*sum(j=1, n\k, j^n));
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a(n) = sum(k=1, n, k^n*(sigma(k, 0)-(n\k)^n));
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a(n) = sum(k=1, n, k^n*sumdiv(k, d, (1-1/d)^n));
Showing 1-3 of 3 results.