A295557 Let d_1, d_2, d_3, ..., d_tau(n) be the divisors of n; a(n) = number of permutations p of d_1, d_2, d_3, ..., d_tau(n) such that p_(i+1)/p_i is a prime or 1/prime for i = 1,2,...,tau(n)-1.

1, 2, 2, 2, 2, 8, 2, 2, 2, 8, 2, 16, 2, 8, 8, 2, 2, 16, 2, 16, 8, 8, 2, 28, 2, 8, 2, 16, 2, 144, 2, 2, 8, 8, 8, 40, 2, 8, 8, 28, 2, 144, 2, 16, 16, 8, 2, 44, 2, 16, 8, 16, 2, 28, 8, 28, 8, 8, 2, 1168, 2, 8, 16, 2, 8, 144, 2, 16, 8, 144, 2, 124, 2, 8, 16, 16, 8, 144

Offset: 1

Author

David A. Corneth and N. J. A. Sloane, Nov 26 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..359

Crossrefs

See A173675 and A179926 for other versions.

Programs

Maple

with(numtheory):
q:= (i, j)-> is(i/j, integer) and isprime(i/j):
b:= proc(s, l) option remember; `if`(s={}, 1, add(
     `if`(q(l, j) or q(j, l), b(s minus{j}, j), 0), j=s))
    end:
a:= n-> ((s-> add(b(s minus {j}, j), j=s))(divisors(n))):
seq(a(n), n=1..100);  # Alois P. Heinz, Nov 26 2017

Mathematica

q[i_, j_] :=  PrimeQ[i/j];
b[s_, l_] := b[s, l] = If[s == {}, 1, Sum[If[q[l, j] || q[j, l], b[s  ~Complement~ {j}, j], 0], {j, s}]];
a[n_] := Function[s, Sum[b[s ~Complement~ {j}, j], {j, s}]][Divisors[n]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 12 2018, after Alois P. Heinz *)