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 A340831 #12 Dec 13 2021 16:14:54
%S A340831 0,0,1,0,1,1,1,0,2,1,1,1,1,1,2,0,1,2,1,2,2,1,1,1,2,1,3,2,1,2,1,0,2,1,
%T A340831 2,3,1,1,2,2,1,3,1,2,4,1,1,1,2,2,2,2,1,4,2,2,2,1,1,4,1,1,4,0,2,3,1,2,
%U A340831 2,2,1,4,1,1,4,2,2,3,1,3,5,1,1,5,2,1,2,3,1,5,2,2,2,1,2,1,1,2,4,4,1,3,1,3,5,1,1,6
%N A340831 Number of factorizations of n into factors > 1 with odd greatest factor.
%H A340831 Antti Karttunen, <a href="/A340831/b340831.txt">Table of n, a(n) for n = 1..20000</a>
%e A340831 The a(n) factorizations for n = 45, 108, 135, 180, 252:
%e A340831 (45) (4*27) (135) (4*45) (4*63)
%e A340831 (5*9) (2*6*9) (3*45) (12*15) (12*21)
%e A340831 (3*15) (3*4*9) (5*27) (4*5*9) (4*7*9)
%e A340831 (3*3*5) (2*2*27) (9*15) (2*2*45) (6*6*7)
%e A340831 (2*2*3*9) (3*5*9) (2*6*15) (2*2*63)
%e A340831 (2*2*3*3*3) (3*3*15) (3*4*15) (2*6*21)
%e A340831 (3*3*3*5) (2*2*5*9) (3*4*21)
%e A340831 (3*3*4*5) (2*2*7*9)
%e A340831 (2*2*3*15) (2*3*6*7)
%e A340831 (2*2*3*3*5) (3*3*4*7)
%e A340831 (2*2*3*21)
%e A340831 (2*2*3*3*7)
%t A340831 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A340831 Table[Length[Select[facs[n],OddQ@*Max]],{n,100}]
%o A340831 (PARI) A340831(n, m=n, fc=1) = if(1==n, !fc, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&(!fc||(d%2)), s += A340831(n/d, d, 0*fc))); (s)); \\ _Antti Karttunen_, Dec 13 2021
%Y A340831 Positions of 0's are A000079.
%Y A340831 The version for partitions is A027193.
%Y A340831 The version for prime indices is A244991.
%Y A340831 The version looking at length instead of greatest factor is A339890.
%Y A340831 The version that also has odd length is A340607.
%Y A340831 The version looking at least factor is A340832.
%Y A340831 - Factorizations -
%Y A340831 A001055 counts factorizations.
%Y A340831 A045778 counts strict factorizations.
%Y A340831 A316439 counts factorizations by product and length.
%Y A340831 A340101 counts factorizations into odd factors, odd-length case A340102.
%Y A340831 A340653 counts balanced factorizations.
%Y A340831 - Odd -
%Y A340831 A000009 counts partitions into odd parts.
%Y A340831 A024429 counts set partitions of odd length.
%Y A340831 A026424 lists numbers with odd Omega.
%Y A340831 A058695 counts partitions of odd numbers.
%Y A340831 A066208 lists numbers with odd-indexed prime factors.
%Y A340831 A067659 counts strict partitions of odd length (A030059).
%Y A340831 A174726 counts ordered factorizations of odd length.
%Y A340831 A340692 counts partitions of odd rank.
%Y A340831 Cf. A026804, A050320, A061395, A339846, A340385, A340596, A340599, A340654, A340655, A340785, A340854, A340855.
%K A340831 nonn
%O A340831 1,9
%A A340831 _Gus Wiseman_, Feb 04 2021
%E A340831 Data section extended up to 108 terms by _Antti Karttunen_, Dec 13 2021