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A356238
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a(n) = Sum_{k=1..n} (k * floor(n/k))^n.
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3
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1, 8, 62, 849, 8541, 206345, 2581403, 76623522, 1617299079, 49463993875, 952905453423, 59000021366675, 1198427462876421, 54128102218676115, 2321105129608323165, 117387839988330848902, 3205342976298888473968, 268263812478494295219717
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k^n * Sum_{d|k} (1 - (1 - 1/d)^n).
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MATHEMATICA
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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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PROG
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(PARI) a(n) = sum(k=1, n, (k*(n\k))^n);
(PARI) a(n) = sum(k=1, n, k^n*sumdiv(k, d, 1-(1-1/d)^n));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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