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 A280152 #10 Feb 16 2025 08:33:38
%S A280152 1,0,0,1,0,1,0,1,1,1,1,1,2,1,2,1,3,2,2,3,3,3,3,4,4,5,4,6,6,6,7,7,9,8,
%T A280152 9,10,11,12,11,14,14,16,15,18,19,19,21,22,25,25,27,28,32,32,34,36,40,
%U A280152 41,42,47,49,52,53,57,62,63,67,71,76,79,82,88,93,98,100,108,114,118,124
%N A280152 Expansion of Product_{k>=1} (1 + floor(1/omega(2*k+1))*x^(2*k+1)), where omega() is the number of distinct prime factors (A001221).
%C A280152 Number of partitions of n into distinct odd prime powers (1 excluded).
%H A280152 G. C. Greubel, <a href="/A280152/b280152.txt">Table of n, a(n) for n = 0..1000</a>
%H A280152 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%H A280152 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A280152 G.f.: Product_{k>=1} (1 + floor(1/omega(2*k+1))*x^(2*k+1)).
%e A280152 a(16) = 3 because we have [13, 3], [11, 5], [9, 7].
%t A280152 nmax = 78; CoefficientList[Series[Product[1 + Floor[1/PrimeNu[2 k + 1]] x^(2 k + 1), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A280152 Cf. A001221, A054685, A061345, A246655, A280151.
%K A280152 nonn
%O A280152 0,13
%A A280152 _Ilya Gutkovskiy_, Dec 27 2016