A254578 Number of ordered factorizations into distinct factors.

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, 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, 11, 3, 13, 1, 5, 3, 13, 1, 29, 1, 3, 5, 5, 3, 13, 1, 21, 3, 3

Offset

1,6

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Arnold Knopfmacher and Michael Mays, Ordered and Unordered Factorizations of Integers, The Mathematica Journal, Vol 10 (1).

Example

a(20)=5 because there are 5 ordered factorizations of 20 into distinct factors: 2*10, 4*5, 5*4, 10*2, 20.

Maple

with(numtheory):
b:= proc(n, i, p) option remember; `if`(n<=i, (p+1)!, 0)+add(
      b(n/d, d-1, p+1), d=select(x->x<=i, divisors(n)minus{1, n}))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 01 2015

Mathematica

f[n_] := f[n] = Level[Table[Map[Prepend[#, d] &, f[n/d]], {d, Rest[Divisors[n]]}], {2}];
f[1] = {{}};
Map[Length, Map[Select[#, Apply[Unequal, #] &] &, Table[f[n], {n, 1, 60}]]]

Crossrefs

Cf. A074206, A254577, A251683.

Sequence in context: A294786 A294787 A294788 * A348610 A296120 A050345

Adjacent sequences: A254575 A254576 A254577 * A254579 A254580 A254581

Keyword

nonn

Author

Geoffrey Critzer, Feb 01 2015

Status

approved