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

1,1

Links

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

Example

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

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 *)

Crossrefs

Cf. A074206, A108501, A108502.

Sequence in context: A253792 A058330 A124256 * A331595 A347288 A324213

Adjacent sequences: A108500 A108501 A108502 * A108504 A108505 A108506

Keyword

nonn

Author

Christian G. Bower, Jun 06 2005

Status

approved