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 A340785 #16 Dec 14 2021 00:24:30
%S A340785 1,2,1,3,1,2,1,5,1,2,1,4,1,2,1,7,1,3,1,4,1,2,1,7,1,2,1,4,1,3,1,11,1,2,
%T A340785 1,6,1,2,1,7,1,3,1,4,1,2,1,12,1,3,1,4,1,3,1,7,1,2,1,7,1,2,1,15,1,3,1,
%U A340785 4,1,3,1,12,1,2,1,4,1,3,1,12,1,2,1,7,1
%N A340785 Number of factorizations of 2n into even factors > 1.
%H A340785 Antti Karttunen, <a href="/A340785/b340785.txt">Table of n, a(n) for n = 1..20000</a>
%F A340785 a(n) = A349906(2*n). - _Antti Karttunen_, Dec 13 2021
%e A340785 The a(n) factorizations for n = 2*2, 2*4, 2*8, 2*12, 2*16, 2*32, 2*36, 2*48 are:
%e A340785 4 8 16 24 32 64 72 96
%e A340785 2*2 2*4 2*8 4*6 4*8 8*8 2*36 2*48
%e A340785 2*2*2 4*4 2*12 2*16 2*32 4*18 4*24
%e A340785 2*2*4 2*2*6 2*2*8 4*16 6*12 6*16
%e A340785 2*2*2*2 2*4*4 2*4*8 2*6*6 8*12
%e A340785 2*2*2*4 4*4*4 2*2*18 2*6*8
%e A340785 2*2*2*2*2 2*2*16 4*4*6
%e A340785 2*2*2*8 2*2*24
%e A340785 2*2*4*4 2*4*12
%e A340785 2*2*2*2*4 2*2*4*6
%e A340785 2*2*2*2*2*2 2*2*2*12
%e A340785 2*2*2*2*6
%t A340785 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A340785 Table[Length[Select[facs[n],Select[#,OddQ]=={}&]],{n,2,100,2}]
%o A340785 (PARI)
%o A340785 A349906(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&!(d%2), s += A349906(n/d, d))); (s));
%o A340785 A340785(n) = A349906(2*n); \\ _Antti Karttunen_, Dec 13 2021
%Y A340785 Note: A-numbers of Heinz-number sequences are in parentheses below.
%Y A340785 The version for partitions is A035363 (A066207).
%Y A340785 The odd version is A340101.
%Y A340785 The even length case is A340786.
%Y A340785 - Factorizations -
%Y A340785 A001055 counts factorizations, with strict case A045778.
%Y A340785 A340653 counts balanced factorizations.
%Y A340785 A340831/A340832 count factorizations with odd maximum/minimum.
%Y A340785 A316439 counts factorizations by product and length
%Y A340785 A340102 counts odd-length factorizations of odd numbers into odd factors.
%Y A340785 - Even -
%Y A340785 A027187 counts partitions of even length/maximum (A028260/A244990).
%Y A340785 A058696 counts partitions of even numbers (A300061).
%Y A340785 A067661 counts strict partitions of even length (A030229).
%Y A340785 A236913 counts partitions of even length and sum.
%Y A340785 A340601 counts partitions of even rank (A340602).
%Y A340785 Cf. A001147, A001222, A050320, A066208, A160786, A174725, A320655, A320656, A339890, A340851.
%Y A340785 Even bisection of A349906.
%K A340785 nonn
%O A340785 1,2
%A A340785 _Gus Wiseman_, Jan 30 2021