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 A382954 #16 Apr 10 2025 08:34:46
%S A382954 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,2,0,1,0,1,3,2,8,1,1,
%T A382954 4,0,14,9,1,4,7,16,26,31,17,3,19,39,54,20,62,9,41,96,89,62,66,34,59,
%U A382954 197,241,289,69,124,184,133,481,440,148,225,394,709,808,984,555,414,799
%N A382954 Number of ways to partition distinct prime numbers into three disjoint sets such that the sum of each set equals n.
%C A382954 Conjecture: a(n) > 0 for n > 35.
%F A382954 a(n) = 1/6 * [(x*y*z)^n] Product_{p prime} (1 + x^p + y^p + z^p) for n > 0.
%e A382954 a(29) = 3: [29; 19, 7, 3; 13, 11, 5], [29; 17, 7, 3, 2; 13, 11, 5], [29; 17, 7, 5; 13, 11, 3, 2].
%e A382954 a(30) = 2: [23, 7; 19, 11; 17, 13], [23, 5, 2; 19, 11; 17, 13].
%Y A382954 Cf. A000607, A258281, A382871.
%K A382954 nonn
%O A382954 0,25
%A A382954 _Seiichi Manyama_, Apr 10 2025