A108501 Number of factorizations of 4*n into even numbers.

2, 3, 2, 5, 2, 4, 2, 7, 3, 4, 2, 7, 2, 4, 3, 11, 2, 6, 2, 7, 3, 4, 2, 12, 3, 4, 3, 7, 2, 7, 2, 15, 3, 4, 3, 12, 2, 4, 3, 12, 2, 7, 2, 7, 4, 4, 2, 19, 3, 6, 3, 7, 2, 8, 3, 12, 3, 4, 2, 14, 2, 4, 4, 22, 3, 7, 2, 7, 3, 7, 2, 21, 2, 4, 4, 7, 3, 7, 2, 19, 4, 4, 2, 14, 3, 4, 3, 12, 2, 11, 3, 7, 3, 4, 3, 30, 2

Offset

1,1

Comments

a(n) = 2 iff n is 1 or an odd prime (A006005); in this case, the two factorizations are 4n = 2 * 2n. - Bernard Schott, Nov 30 2020

Links

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

Formula

a(2^k) = A000041(k+2). - Bernard Schott, Dec 01 2020

Example

a(6)=4 because 6*4=24 can be factored as 24=12*2=6*4=6*2*2.

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, 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, 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 *)

Crossrefs

Cf. A000041, A001055, A006005, A108502, A108503.

Sequence in context: A073751 A319431 A258581 * A166226 A263978 A326810

Adjacent sequences: A108498 A108499 A108500 * A108502 A108503 A108504

Keyword

nonn

Author

Christian G. Bower, Jun 06 2005

Status

approved