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A254578 Number of ordered factorizations into distinct factors.

%I A254578 #9 Feb 01 2015 19:33:58
%S A254578 1,1,1,1,1,3,1,3,1,3,1,5,1,3,3,3,1,5,1,5,3,3,1,13,1,3,3,5,1,13,1,5,3,
%T A254578 3,3,13,1,3,3,13,1,13,1,5,5,3,1,21,1,5,3,5,1,13,3,13,3,3,1,29,1,3,5,
%U A254578 11,3,13,1,5,3,13,1,29,1,3,5,5,3,13,1,21,3,3
%N A254578 Number of ordered factorizations into distinct factors.
%H A254578 Alois P. Heinz, <a href="/A254578/b254578.txt">Table of n, a(n) for n = 1..10000</a>
%H A254578 Arnold Knopfmacher and Michael Mays, <a href="http://www.mathematica-journal.com/issue/v10i1/contents/Factorizations/Factorizations_3.html">Ordered and Unordered Factorizations of Integers</a>, The Mathematica Journal, Vol 10 (1).
%e A254578 a(20)=5 because there are 5 ordered factorizations of 20 into distinct factors: 2*10, 4*5, 5*4, 10*2, 20.
%p A254578 with(numtheory):
%p A254578 b:= proc(n, i, p) option remember; `if`(n<=i, (p+1)!, 0)+add(
%p A254578       b(n/d, d-1, p+1), d=select(x->x<=i, divisors(n)minus{1, n}))
%p A254578     end:
%p A254578 a:= n-> b(n$2, 0):
%p A254578 seq(a(n), n=1..100);  # _Alois P. Heinz_, Feb 01 2015
%t A254578 f[n_] := f[n] = Level[Table[Map[Prepend[#, d] &, f[n/d]], {d,Rest[Divisors[n]]}], {2}];
%t A254578 f[1] = {{}};
%t A254578 Map[Length,Map[Select[#, Apply[Unequal, #] &] &, Table[f[n], {n, 1, 60}]]]
%Y A254578 Cf. A074206, A254577, A251683.
%K A254578 nonn
%O A254578 1,6
%A A254578 _Geoffrey Critzer_, Feb 01 2015