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 A345686 a(n) = n! * Sum_{k=1..n} n/floor(n/k)^2. 1
 1, 5, 38, 222, 1974, 14640, 154580, 1476720, 17753400, 205430400, 2924030592, 38559628800, 623916216000, 9701871379200, 172359487872000, 3007238402488320, 60362232844193280, 1161408374590464000, 25603215951785472000, 547592177551491072000, 12990145748633044992000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..21. Mathoverflow, An asymptotic formula for a sum involving powers of floor functions, 2019. FORMULA a(n) ~ c * n^2 * n!, where c = Sum_{j>-1} 1/(j^3*(j+1)) = zeta(3) - Pi^2/6 + 1. MATHEMATICA Table[n! * Sum[n/Floor[n/k]^2, {k, 1, n}], {n, 1, 25}] Table[n*n!*(Sum[(Floor[n/j] - Floor[n/(j + 1)])/j^2, {j, 1, n}]), {n, 1, 25}] CROSSREFS Cf. A345683. Sequence in context: A318102 A163698 A294053 * A279265 A129048 A279489 Adjacent sequences: A345683 A345684 A345685 * A345687 A345688 A345689 KEYWORD nonn AUTHOR Vaclav Kotesovec, Jun 23 2021 STATUS approved

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Last modified February 20 21:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)