A108503 Number of ordered factorizations of 4*n into even numbers.

2, 4, 3, 8, 3, 8, 3, 16, 4, 8, 3, 20, 3, 8, 5, 32, 3, 13, 3, 20, 5, 8, 3, 48, 4, 8, 5, 20, 3, 18, 3, 64, 5, 8, 5, 38, 3, 8, 5, 48, 3, 18, 3, 20, 7, 8, 3, 112, 4, 13, 5, 20, 3, 19, 5, 48, 5, 8, 3, 56, 3, 8, 7, 128, 5, 18, 3, 20, 5, 18, 3, 104, 3, 8, 7, 20, 5, 18, 3, 112, 6, 8, 3, 56, 5, 8, 5, 48

Offset: 1

Author

Christian G. Bower, Jun 06 2005

Keywords

• nonn

Examples

			a(9)=4 because 9*4=36 can be factored as 36=18*2=2*18=6*6.
		

Links

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

Crossrefs

Cf. A074206, A108501, A108502.

Programs

Maple

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

Mathematica

nn = 300;f[list_, i] := list[[i]];a = Table[Boole[EvenQ[n]], {n, 1, nn}];Select[Map[Total, Transpose[NestList[Table[DirichletConvolve[f[#, n], f[a, n], n, m], {m, 1, nn}] &, a, nn]]], # > 1 &] (* Geoffrey Critzer, Feb 17 2015 *)