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%I #8 Feb 17 2015 17:12:41
%S 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,
%T 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,
%U 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
%N Number of ordered factorizations of 4*n into even numbers.
%H Alois P. Heinz, <a href="/A108503/b108503.txt">Table of n, a(n) for n = 1..10000</a>
%e a(9)=4 because 9*4=36 can be factored as 36=18*2=2*18=6*6.
%p with(numtheory):
%p b:= proc(n) option remember; 1+add(`if`(irem(d, 2)=0 and
%p irem(n/d, 2)=0, b(d), 0), d=divisors(n) minus {1, n})
%p end:
%p a:= n-> b(4*n):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Feb 17 2015
%t 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 *)
%Y Cf. A074206, A108501, A108502.
%K nonn
%O 1,1
%A _Christian G. Bower_, Jun 06 2005
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