cp's OEIS Frontend

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.

%I A073090 #28 Mar 06 2025 01:20:58
%S A073090 1,1,1,1,2,2,8,8,22,104,1128,1128,14520,14520,229734,3217088,21157428,
%T A073090 21157428
%N 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.
%F A073090 For each prime p: a(p) = a(p-1). - _Alois P. Heinz_, Nov 08 2021
%e A073090 p(1,2)=(1,2) is the only permutation such that 1/p(1)+2/p(2) is an integer hence a(2)=1.
%e A073090 a(4) = 2: 1234, 2431.
%e A073090 a(5) = 2: 12345, 24315.
%e A073090 a(6) = 8: 123456, 146253, 216453, 243156, 312654, 342651, 621354, 641352.
%e A073090 a(7) = 8: 1234567, 1462537, 2164537, 2431567, 3126547, 3426517, 6213547, 6413527.
%o A073090 (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)))
%Y A073090 Cf. A000040, A349257.
%K A073090 nonn,more
%O A073090 0,5
%A A073090 _Benoit Cloitre_, Aug 18 2002
%E A073090 More terms from _John W. Layman_, Feb 06 2004
%E A073090 Corrected by _Benoit Cloitre_, Feb 21 2004
%E A073090 a(14)-a(15) from _Matthijs Coster_, Mar 22 2017
%E A073090 a(0)=1 prepended by _Alois P. Heinz_, Nov 08 2021
%E A073090 a(16)-a(17) from _Jinyuan Wang_, Mar 05 2025