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 A378222 #13 May 01 2025 08:24:25 %S A378222 1,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,1,2,1,1,3,1,1,1,2,1,4,1,1,3,1,1,3,1, %T A378222 3,2,1,1,3,1,1,3,1,1,8,1,1,1,2,2,3,1,1,4,3,1,3,1,1,3,1,1,8,1,3,3,1,1, %U A378222 3,3,1,2,1,1,8,1,3,3,1,1,8,1,1,3,3,1,3,1,1,8,3,1,3,1,3,1,1,2,8,2,1,3,1,1,13 %N A378222 Number of ordered factorizations of the odd part of n into factors > 1. %H A378222 Antti Karttunen, <a href="/A378222/b378222.txt">Table of n, a(n) for n = 1..20000</a> %F A378222 a(n) = A074206(A000265(n)). %F A378222 For all n >= 1, a(2n) = a(n). %F A378222 For all n >= 0, a(2n+1) = A352063(n) = A002033(2*n) = A074206(2*n+1). %t A378222 f[1] = 1; f[n_] := f[n] = DivisorSum[n, f[#] &, # < n &]; a[n_] := f[n/2^IntegerExponent[n, 2]]; Array[a, 100] (* _Amiram Eldar_, May 01 2025 *) %o A378222 (PARI) %o A378222 A000265(n) = (n>>valuation(n,2)); %o A378222 A074206(n) = if(n>1, sumdiv(n, i, if(i<n, A074206(i))), n); \\ From A074206 %o A378222 A378222(n) = A074206(A000265(n)); %Y A378222 Cf. A000265, A002033, A074206. %Y A378222 Bisections: A352063, and the sequence itself. %K A378222 nonn,easy %O A378222 1,9 %A A378222 _Antti Karttunen_, Nov 24 2024