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 A339553 #5 Feb 16 2025 08:34:01
%S A339553 1,0,0,1,0,0,0,1,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,3,0,0,
%T A339553 0,3,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,
%U A339553 0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,8
%N A339553 Number of ordered factorizations of n into perfect powers > 1.
%H A339553 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>
%F A339553 a(1) = 1; a(n) = Sum_{d|n, d<n} A075802(n/d) * a(d).
%t A339553 a[n_] := If[n == 1, n, Sum[If[d < n, Boole[GCD @@ FactorInteger[n/d][[All, 2]] > 1] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 128}]
%Y A339553 Cf. A001597, A050363, A052485 (positions of 0's), A075802, A294068.
%K A339553 nonn
%O A339553 1,16
%A A339553 _Ilya Gutkovskiy_, Dec 08 2020