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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.
2
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
1,2
LINKS
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 *)
CROSSREFS
See A173675 and A179926 for other versions.
Sequence in context: A054083 A270379 A337358 * A327641 A066874 A087577
KEYWORD
nonn
AUTHOR
STATUS
approved