%I #26 Nov 13 2021 06:00:06
%S 1,0,1,0,0,1,1,0,0,1,0,0,0,0,2,1,1,2,2,0,2,0,0,0,0,0,0,8,4,4,2,2,0,2,
%T 0,8,18,18,14,18,0,14,0,0,22,113,130,102,135,108,122,0,314,0,104,0,0,
%U 0,0,0,0,0,0,0,0,1128,1152,1166,1130,1078,1334,1182,0,1734,3390,1226,0,1128,0,0,0,0,0,0,0,0,0,0,0,0,14520
%N Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) is the number of permutations p of [n] such that Sum_{j=1..n} j/p(j) is an integer and p(n) = k.
%F If n is prime, T(n,k) = 0 for 1 <= k <= n1.
%F T(n,n) = A073090(n1).
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, 0, 1;
%e 1, 0, 0, 1;
%e 0, 0, 0, 0, 2;
%e 1, 1, 2, 2, 0, 2;
%e 0, 0, 0, 0, 0, 0, 8;
%e 4, 4, 2, 2, 0, 2, 0, 8;
%e 18, 18, 14, 18, 0, 14, 0, 0, 22;
%e 113, 130, 102, 135, 108, 122, 0, 314, 0, 104;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1128;
%o (Ruby)
%o def A(n)
%o ary = Array.new(n, 0)
%o (1..n).to_a.permutation{i
%o ary[i[1]  1] += 1 if (1..n).inject(0){s, j s + j / i[j  1].to_r}.denominator == 1
%o }
%o ary
%o end
%o def A349277(n)
%o (1..n).map{i A(i)}.flatten
%o end
%o p A349277(8)
%Y Row sum gives A073090.
%K nonn,tabl
%O 1,15
%A _Seiichi Manyama_, Nov 12 2021
