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 A308063 #14 Jul 03 2025 04:07:01
%S A308063 1,1,1,2,1,2,1,4,2,2,1,5,1,2,2,8,1,5,1,5,2,2,1,12,2,2,4,5,1,7,1,16,2,
%T A308063 2,2,14,1,2,2,12,1,7,1,5,5,2,1,28,2,5,2,5,1,12,2,12,2,2,1,21,1,2,5,32,
%U A308063 2,7,1,5,2,7,1,37,1,2,5,5,2,7,1,28,8,2,1,21,2,2,2,12,1,21
%N A308063 Number of ordered factorizations of n into numbers with an odd number of distinct prime divisors.
%H A308063 Amiram Eldar, <a href="/A308063/b308063.txt">Table of n, a(n) for n = 1..10000</a>
%F A308063 G.f. A(x) satisfies: A(x) = x + Sum_{k>=1} A(x^A030230(k)).
%F A308063 a(1) = 1; a(n) = Sum_{d|n, d<n} A092248(n/d)*a(d).
%F A308063 a(n) = 1 if n is in A008578.
%t A308063 terms = 90; A[_] = 0; Do[A[x_] = x + Sum[Boole[OddQ[PrimeNu[k]]] A[x^k], {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
%t A308063 f[n_] := f[n] = Boole[OddQ[PrimeNu[n]]]; a[n_] := If[n == 1, n, Sum[If[d < n, f[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 90}]
%o A308063 (PARI) a(n) = if(n == 1, 1, sumdiv(n, d, if(d<n, (omega(n/d) % 2) * a(d)))); \\ _Amiram Eldar_, Jul 03 2025
%Y A308063 Cf. A008578, A030230, A050334, A074206, A092248.
%K A308063 nonn
%O A308063 1,4
%A A308063 _Ilya Gutkovskiy_, May 10 2019