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A356240 a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^n. 1
0, 1, 9, 114, 1332, 25404, 395460, 9724901, 207584371, 6120938951, 151737244257, 5932533980409, 168400694345669, 7145593797561899, 260681076993636793, 12410128414690753548, 473029927456547840472, 27572016889372245275679 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{k=1..n} k^n * (sigma_0(k) - floor(n/k)^n) = A356239(n) - A356238(n).
a(n) = Sum_{k=1..n} k^n * Sum_{d|k} (1 - 1/d)^n.
MATHEMATICA
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 *)
PROG
(PARI) a(n) = sum(k=1, n, (k-1)^n*sum(j=1, n\k, j^n));
(PARI) a(n) = sum(k=1, n, k^n*(sigma(k, 0)-(n\k)^n));
(PARI) a(n) = sum(k=1, n, k^n*sumdiv(k, d, (1-1/d)^n));
CROSSREFS
Sequence in context: A243676 A012116 A362576 * A157551 A157570 A223499
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 30 2022
STATUS
approved

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Last modified April 17 18:43 EDT 2024. Contains 371765 sequences. (Running on oeis4.)