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A344724 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^n. 4
1, 3, 27, 240, 3094, 45990, 821484, 16711680, 387177517, 9990293423, 285263019633, 8913939911695, 302862111412779, 11111328866154037, 437889173336927557, 18446462747068745474, 827238010832411671962, 39346258082152478030126 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=1,..n} Sum_{d|k} (-1)^(k/d + 1) * (d^n - (d - 1)^n).
a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 + x^k).
a(n) ~ n^n. - Vaclav Kotesovec, May 28 2021
MATHEMATICA
a[n_] := Sum[(-1)^(k + 1) * Quotient[n, k]^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, May 27 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n\k)^n);
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*(d^n-(d-1)^n)));
CROSSREFS
Main diagonal of A344726.
Cf. A332469.
Sequence in context: A221769 A065100 A035088 * A268094 A013708 A102518
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 27 2021
STATUS
approved

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Last modified July 18 01:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)