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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 Table of n, a(n) for n=1..18. 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 Cf. A356131, A356238, A356239, A356244. Sequence in context: A243676 A012116 A362576 * A157551 A157570 A223499 Adjacent sequences: A356237 A356238 A356239 * A356241 A356242 A356243 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.)