This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339846 #18 Oct 22 2023 15:15:09
%S A339846 1,0,0,1,0,1,0,1,1,1,0,2,0,1,1,3,0,2,0,2,1,1,0,4,1,1,1,2,0,3,0,3,1,1,
%T A339846 1,5,0,1,1,4,0,3,0,2,2,1,0,6,1,2,1,2,0,4,1,4,1,1,0,6,0,1,2,6,1,3,0,2,
%U A339846 1,3,0,8,0,1,2,2,1,3,0,6,3,1,0,6,1,1,1,4,0,6,1,2,1,1,1,10,0,2,2,5,0,3,0,4,3
%N A339846 Number of even-length factorizations of n into factors > 1.
%H A339846 Antti Karttunen, <a href="/A339846/b339846.txt">Table of n, a(n) for n = 1..65537</a>
%H A339846 Gus Wiseman, <a href="/A339741/a339741_1.txt">Counting and ranking factorizations, factorability, and vertex-degree partitions for groupings into pairs.</a>
%H A339846 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A339846 a(n) + A339890(n) = A001055(n).
%e A339846 The a(n) factorizations for n = 12, 16, 24, 36, 48, 72, 96, 120:
%e A339846 2*6 2*8 3*8 4*9 6*8 8*9 2*48 2*60
%e A339846 3*4 4*4 4*6 6*6 2*24 2*36 3*32 3*40
%e A339846 2*2*2*2 2*12 2*18 3*16 3*24 4*24 4*30
%e A339846 2*2*2*3 3*12 4*12 4*18 6*16 5*24
%e A339846 2*2*3*3 2*2*2*6 6*12 8*12 6*20
%e A339846 2*2*3*4 2*2*2*9 2*2*3*8 8*15
%e A339846 2*2*3*6 2*2*4*6 10*12
%e A339846 2*3*3*4 2*3*4*4 2*2*5*6
%e A339846 2*2*2*12 2*3*4*5
%e A339846 2*2*2*2*2*3 2*2*2*15
%e A339846 2*2*3*10
%p A339846 g:= proc(n, k, t) option remember; `if`(n>k, 0, t)+
%p A339846 `if`(isprime(n), 0, add(`if`(d>k, 0, g(n/d, d, 1-t)),
%p A339846 d=numtheory[divisors](n) minus {1, n}))
%p A339846 end:
%p A339846 a:= n-> `if`(n=1, 1, g(n$2, 0)):
%p A339846 seq(a(n), n=1..100); # _Alois P. Heinz_, Dec 30 2020
%t A339846 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A339846 Table[Length[Select[facs[n],EvenQ@Length[#]&]],{n,100}]
%o A339846 (PARI) A339846(n, m=n, e=1) = if(1==n, e, sumdiv(n, d, if((d>1)&&(d<=m), A339846(n/d, d, 1-e)))); \\ _Antti Karttunen_, Oct 22 2023
%Y A339846 The case of set partitions (or n squarefree) is A024430.
%Y A339846 The case of partitions (or prime powers) is A027187.
%Y A339846 The ordered version is A174725, odd: A174726.
%Y A339846 The odd-length factorizations are counted by A339890.
%Y A339846 A001055 counts factorizations, with strict case A045778.
%Y A339846 A001358 lists semiprimes, with squarefree case A006881.
%Y A339846 A027187 counts partitions of even length, ranked by A028260.
%Y A339846 A058696 counts partitions of even numbers, ranked by A300061.
%Y A339846 A316439 counts factorizations by product and length.
%Y A339846 A340102 counts odd-length factorizations into odd factors.
%Y A339846 Cf. A002033, A007716, A027193, A050320, A058695, A074206, A236913, A320655, A320656, A320732.
%K A339846 nonn
%O A339846 1,12
%A A339846 _Gus Wiseman_, Dec 28 2020
%E A339846 Data section extended up to a(105) by _Antti Karttunen_, Oct 22 2023