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 A073090 Number of permutations p from (1,2,3,...,n) to (1,2,3...,n) such that 1/p(1)+2/p(2)+...+n/p(n) is an integer. 3
 1, 1, 1, 1, 2, 2, 8, 8, 22, 104, 1128, 1128, 14520, 14520, 229734, 3217088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Table of n, a(n) for n=0..15. FORMULA For each prime p: a(p) = a(p-1). - Alois P. Heinz, Nov 08 2021 EXAMPLE p(1,2)=(1,2) is the only permutation such that 1/p(1)+2/p(2) is an integer hence a(2)=1. a(4) = 2: 1234, 2431. a(5) = 2: 12345, 24315. a(6) = 8: 123456, 146253, 216453, 243156, 312654, 342651, 621354, 641352. a(7) = 8: 1234567, 1462537, 2164537, 2431567, 3126547, 3426517, 6213547, 6413527. PROG (PARI) a(n)=if(n<0, 0, sum(k=1, n!, if(frac(sum(i=1, n, i/component(numtoperm(n, k), i))), 0, 1))) CROSSREFS Cf. A000040. Sequence in context: A082887 A137583 A099328 * A120544 A155950 A162959 Adjacent sequences: A073087 A073088 A073089 * A073091 A073092 A073093 KEYWORD nonn,more AUTHOR Benoit Cloitre, Aug 18 2002 EXTENSIONS More terms from John W. Layman, Feb 06 2004 Corrected by Benoit Cloitre, Feb 21 2004 a(14)-a(15) from Matthijs Coster, Mar 22 2017 a(0)=1 prepended by Alois P. Heinz, Nov 08 2021 STATUS approved

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Last modified September 19 09:52 EDT 2024. Contains 376008 sequences. (Running on oeis4.)