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 A284171 #15 Feb 16 2025 08:33:43
%S A284171 1,1,0,0,1,1,0,0,1,2,1,0,1,2,1,0,1,2,1,0,1,2,1,0,1,3,2,1,2,3,2,1,2,3,
%T A284171 3,2,4,5,3,2,4,5,3,2,4,6,4,2,4,7,5,2,5,8,5,2,5,8,6,3,5,10,8,4,6,10,8,
%U A284171 4,6,10,9,5,7,11,10,6,8,12,10,6,8,13,11,7,9,15,13,7,10,16,14,8,10,16,15,9,10,17,16,9,11
%N A284171 Number of partitions of n into distinct perfect powers (including 1).
%C A284171 Differs from the sequence A112345 which does not consider 1 as a perfect power.
%H A284171 Vaclav Kotesovec, <a href="/A284171/b284171.txt">Table of n, a(n) for n = 0..10000</a>
%H A284171 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>
%H A284171 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A284171 G.f.: Product_{k>=1} (1 + x^A001597(k)).
%F A284171 a(n) = A112345(n-1) + A112345(n).
%e A284171 a(25) = 3 because we have [25], [16, 9] and [16, 8, 1].
%t A284171 nmax = 100; CoefficientList[Series[(1 + x) Product[(1 + Boole[GCD @@ FactorInteger[k][[All, 2]] > 1] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%o A284171 (PARI) Vec((1 + x) * prod(k=1, 100, 1 + (gcd(factorint(k)[,2])>1)*x^k) + O(x^101)) \\ _Indranil Ghosh_, Mar 21 2017
%Y A284171 Cf. A001597, A078635, A112344, A112345.
%K A284171 nonn
%O A284171 0,10
%A A284171 _Ilya Gutkovskiy_, Mar 21 2017