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.

1, 1, 1, 1, 2, 2, 8, 8, 22, 104, 1128, 1128, 14520, 14520, 229734, 3217088

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