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 A259196 #29 Mar 01 2025 22:49:37
%S A259196 1,1,1,2,2,3,4,3,4,5,6,6,8,7,10,10,12,11,16,12,19,17,22,18,26,20,31,
%T A259196 24,33,27,42,29,47,35,51,38,60,41,68,47,73,53,86,54,95,64,103,70,116,
%U A259196 73,131,81,137,89,156,92,171,103,180,112,202,117,223,127,232
%N A259196 Number of partitions of n into six primes.
%H A259196 Alois P. Heinz, <a href="/A259196/b259196.txt">Table of n, a(n) for n = 12..10000</a>
%H A259196 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A259196 a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(n-i-j-k-l-m). - _Wesley Ivan Hurt_, Apr 17 2019
%F A259196 a(n) = [x^n y^6] Product_{k>=1} 1/(1 - y*x^prime(k)). - _Ilya Gutkovskiy_, Apr 18 2019
%e A259196 a(17) = 3 because there are 3 partitions of 17 into six primes: [2,2,2,2,2,7], [2,2,2,3,3,5] and [2,3,3,3,3,3].
%t A259196 Table[Count[IntegerPartitions[n,{6}],_?(AllTrue[#,PrimeQ]&)],{n,12,80}] (* _Harvey P. Dale_, Jul 27 2024 *)
%Y A259196 Column k=6 of A117278.
%Y A259196 Number of partitions of n into r primes for r = 1-10: A010051, A061358, A068307, A259194, A259195, this sequence, A259197, A259198, A259200, A259201.
%Y A259196 Cf. A000040.
%K A259196 nonn,easy
%O A259196 12,4
%A A259196 _Doug Bell_, Jun 20 2015