A108502 Number of factorizations of 4*n into distinct even numbers.

1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 5, 2, 3, 3, 4, 2, 4, 2, 5, 3, 3, 2, 7, 2, 3, 3, 5, 2, 6, 2, 5, 3, 3, 3, 7, 2, 3, 3, 7, 2, 6, 2, 5, 4, 3, 2, 10, 2, 4, 3, 5, 2, 6, 3, 7, 3, 3, 2, 11, 2, 3, 4, 6, 3, 6, 2, 5, 3, 6, 2, 11, 2, 3, 4, 5, 3, 6, 2, 10, 3, 3, 2, 11, 3, 3, 3, 7, 2, 9, 3, 5, 3, 3, 3, 14, 2, 4, 4, 7, 2, 6

Offset: 1

Author

Christian G. Bower, Jun 06 2005

Keywords

• nonn

Examples

			a(15)=3 because 15*4=60 can be factored as 60=30*2=10*6.
		

Links

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

Crossrefs

Cf. A045778, A108501, A108503.

Programs

Maple

with(numtheory):
b:= proc(n, i) option remember; `if`(n<=i, 1, 0)+
      add(`if`(d<=i and irem(d, 2)=0 and irem(n/d, 2)=0,
      b(n/d, min(d-1, i)), 0), d=divisors(n) minus {1, n})
    end:
a:= n-> b(4*n$2):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 17 2015

Mathematica

b[n_, i_] := b[n, i] = If[n <= i, 1, 0] + Sum[If[d <= i && Mod[d, 2]==0 && Mod[n/d, 2]==0, b[n/d, Min[d-1, i]], 0], {d, Divisors[n][[2 ;; -2]]}];
a[n_] := b[4n, 4n];
Array[a, 100] (* Jean-François Alcover, Nov 05 2020, after Alois P. Heinz *)