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 A281274 #6 Feb 16 2025 08:33:39
%S A281274 1,0,1,0,0,1,0,1,0,0,1,0,1,0,0,1,0,2,0,1,0,0,1,0,1,0,0,1,1,1,1,0,1,1,
%T A281274 1,1,0,0,1,0,1,1,0,2,0,2,1,1,1,0,1,1,1,1,0,1,1,1,3,0,3,0,1,2,0,2,0,0,
%U A281274 2,1,2,1,0,2,1,3,1,2,0,2,1,1,2,0,2,1,3,2,2,1,1,2,2,2,2,0,3,0,2,2,1,4,1,3,2,3,2,2,1,2,3
%N A281274 Expansion of Product_{j>=1} (1 + x^(Sum_{i=1..j} prime(i))).
%C A281274 Number of partitions of n into distinct nonzero partial sums of primes (A007504).
%H A281274 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>
%H A281274 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePartition.html">Prime Partition</a>
%H A281274 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A281274 G.f.: Product_{j>=1} (1 + x^(Sum_{i=1..j} prime(i))).
%e A281274 a(17) = 2 because we have [17] and [10, 5, 2], where 2 = prime(1), 5 = prime(1) + prime(2), 10 = prime(1) + prime(2) + prime(3), 17 = prime(1) + prime(2) + prime(3) + prime(4).
%t A281274 nmax = 110; CoefficientList[Series[Product[1 + x^Sum[Prime[i], {i, 1, j}], {j, 1, nmax}], {x, 0, nmax}], x]
%Y A281274 Cf. A000586, A000607, A007504, A281273.
%K A281274 nonn
%O A281274 0,18
%A A281274 _Ilya Gutkovskiy_, Jan 18 2017