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

1,2

Links

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

Example

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

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 *)

Crossrefs

Cf. A045778, A108501, A108503.

Sequence in context: A010553 A262095 A163374 * A260235 A078120 A057525

Adjacent sequences: A108499 A108500 A108501 * A108503 A108504 A108505

Keyword

nonn

Author

Christian G. Bower, Jun 06 2005

Status

approved