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 A307825 #6 Apr 30 2019 21:50:13 %S A307825 0,0,0,0,0,0,0,0,0,1,1,1,2,2,4,4,5,4,6,5,7,6,8,8,10,8,10,9,12,11,12, %T A307825 11,15,12,15,14,17,17,20,18,19,19,19,22,23,20,21,24,23,24,24,24,27,28, %U A307825 24,27,28,28,28,33,27,33,29,31,30,35,27,35,33,34,31,40,32,42,35,39,35,47,32 %N A307825 Number of partitions of n into 3 distinct prime powers (not including 1). %H A307825 <a href="/index/Par#part">Index entries for sequences related to partitions</a> %F A307825 a(n) = [x^n y^3] Product_{k>=1} (1 + y*x^A246655(k)). %e A307825 a(15) = 4 because we have [9, 4, 2], [8, 5, 2], [8, 4, 3] and [7, 5, 3]. %t A307825 Table[Count[IntegerPartitions[n, {3}], _?(And[UnsameQ @@ #, AllTrue[#, PrimePowerQ[#] &]] &)], {n, 0, 78}] %Y A307825 Cf. A000961, A106244, A125688, A246655, A306433, A307727. %K A307825 nonn %O A307825 0,13 %A A307825 _Ilya Gutkovskiy_, Apr 30 2019