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%I #8 Nov 05 2020 15:07:28
%S 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,
%T 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,
%U 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
%N Number of factorizations of 4*n into distinct even numbers.
%H Alois P. Heinz, <a href="/A108502/b108502.txt">Table of n, a(n) for n = 1..10000</a>
%e a(15)=3 because 15*4=60 can be factored as 60=30*2=10*6.
%p with(numtheory):
%p b:= proc(n, i) option remember; `if`(n<=i, 1, 0)+
%p add(`if`(d<=i and irem(d, 2)=0 and irem(n/d, 2)=0,
%p b(n/d, min(d-1, i)), 0), d=divisors(n) minus {1, n})
%p end:
%p a:= n-> b(4*n$2):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Feb 17 2015
%t 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]]}];
%t a[n_] := b[4n, 4n];
%t Array[a, 100] (* _Jean-François Alcover_, Nov 05 2020, after _Alois P. Heinz_ *)
%Y Cf. A045778, A108501, A108503.
%K nonn
%O 1,2
%A _Christian G. Bower_, Jun 06 2005
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