

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
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..15.


FORMULA

For each prime p: a(p) = a(p1).  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



