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Number of integer factorizations of n into distinct even factors.
1

%I #6 Oct 23 2022 23:55:40

%S 1,1,0,1,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,3,0,1,

%T 0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,3,0,1,0,4,0,1,0,2,

%U 0,1,0,4,0,1,0,2,0,1,0,5,0,1,0,3,0,1,0

%N Number of integer factorizations of n into distinct even factors.

%e The factorizations of 36..48 are (empty columns indicated by dots):

%e 36 . 38 . 40 . 42 . 44 . 46 . 48

%e 2*18 2*20 2*22 6*8

%e 4*10 2*24

%e 4*12

%e 2*4*6

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t Table[Length[Select[facs[n],UnsameQ@@#&&OddQ[Times@@(#+1)]&]],{n,100}]

%Y The non-strict version is A349906.

%Y Same as A357859 with zeros every other term.

%Y A000005 counts divisors.

%Y A001055 counts factorizations.

%Y A001221 counts distinct prime factors, sum A001414.

%Y A001222 counts prime-power divisors.

%Y A050361 counts strict factorizations into prime powers.

%Y Cf. A000009, A000688, A000961, A023894, A295935, A318721, A340785.

%K nonn

%O 1,8

%A _Gus Wiseman_, Oct 17 2022