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 A352063 #25 Feb 16 2025 08:34:03
%S A352063 1,1,1,1,2,1,1,3,1,1,3,1,2,4,1,1,3,3,1,3,1,1,8,1,2,3,1,3,3,1,1,8,3,1,
%T A352063 3,1,1,8,3,1,8,1,3,3,1,3,3,3,1,8,1,1,13,1,1,3,1,3,8,3,2,3,4,1,3,1,3,
%U A352063 20,1,1,3,3,3,8,1,1,8,3,1,3,3,1,13,1,2,8,1,8,3,1,1,3,3,3,20,1,1,13,1,1,3,3,3,8,3,1
%N A352063 Number of ordered factorizations of 2*n + 1 into odd factors > 1.
%C A352063 Also number of perfect partitions of 2*n.
%H A352063 Antti Karttunen, <a href="/A352063/b352063.txt">Table of n, a(n) for n = 0..20000</a>
%H A352063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPartition.html">Perfect Partition</a>
%H A352063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OrderedFactorization.html">Ordered Factorization</a>
%F A352063 a(n) = A002033(2*n) = A074206(2*n+1).
%F A352063 a(n) = A378222(2*n+1) = A074206(A064216(1+n)). - _Antti Karttunen_, Nov 24 2024
%t A352063 A074206[1] = 1; A074206[n_] := A074206[n] = Sum[If[d < n, A074206[d], 0], {d, Divisors[n]}]; a[n_] := A074206[2 n + 1]; Table[a[n], {n, 0, 90}]
%o A352063 (PARI)
%o A352063 A074206(n) = if(n>1, sumdiv(n, i, if(i<n, A074206(i))), n); \\ From A074206
%o A352063 A352063(n) = A074206(1+n+n); \\ _Antti Karttunen_, Nov 24 2024
%Y A352063 Cf. A002033, A058696, A064216, A074206, A108503, A340101, A349907, A378222.
%K A352063 nonn
%O A352063 0,5
%A A352063 _Ilya Gutkovskiy_, Mar 04 2022
%E A352063 More terms from _Antti Karttunen_, Nov 24 2024