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 A237669 #21 Jan 24 2018 03:26:13
%S A237669 0,5,12,17,29,35,50,59,77,87,108,120,144,156,182,198,228,243,275,292,
%T A237669 327,346,383,402,443,465,507,531,578,601,649,674,722,748,800,829,886,
%U A237669 915,974,1006,1067,1097,1158,1189,1253,1286,1353,1388,1456,1491,1561
%N A237669 Number of prime parts in the partitions of 3n into 3 parts.
%H A237669 Vincenzo Librandi, <a href="/A237669/b237669.txt">Table of n, a(n) for n = 1..300</a>
%H A237669 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A237669 a(n) = A237264(n) + A236762(n) + A236758(n).
%e A237669 Count the primes in the partitions of 3n into 3 parts for a(n).
%e A237669 13 + 1 + 1
%e A237669 12 + 2 + 1
%e A237669 11 + 3 + 1
%e A237669 10 + 4 + 1
%e A237669 9 + 5 + 1
%e A237669 8 + 6 + 1
%e A237669 7 + 7 + 1
%e A237669 10 + 1 + 1 11 + 2 + 2
%e A237669 9 + 2 + 1 10 + 3 + 2
%e A237669 8 + 3 + 1 9 + 4 + 2
%e A237669 7 + 4 + 1 8 + 5 + 2
%e A237669 6 + 5 + 1 7 + 6 + 2
%e A237669 7 + 1 + 1 8 + 2 + 2 9 + 3 + 3
%e A237669 6 + 2 + 1 7 + 3 + 2 8 + 4 + 3
%e A237669 5 + 3 + 1 6 + 4 + 2 7 + 5 + 3
%e A237669 4 + 4 + 1 5 + 5 + 2 6 + 6 + 3
%e A237669 4 + 1 + 1 5 + 2 + 2 6 + 3 + 3 7 + 4 + 4
%e A237669 3 + 2 + 1 4 + 3 + 2 5 + 4 + 3 6 + 5 + 4
%e A237669 1 + 1 + 1 2 + 2 + 2 3 + 3 + 3 4 + 4 + 4 5 + 5 + 5
%e A237669 3(1) 3(2) 3(3) 3(4) 3(5) .. 3n
%e A237669 ---------------------------------------------------------------------
%e A237669 0 5 12 17 29 .. a(n)
%t A237669 Table[Sum[Sum[PrimePi[i] - PrimePi[i - 1], {i, n + Floor[j/2] + 1 - Floor[1/(j + 1)], n + 2 (j + 1)}], {j, 0, n - 2}] + Sum[i (PrimePi[i] - PrimePi[i - 1]), {i, n}] + Sum[(PrimePi[n + i] - PrimePi[n + i - 1]) (n - 2 i), {i, Floor[(n - 1)/2]}] + Sum[(PrimePi[i] - PrimePi[i - 1]) (2 n - 2 i + 1 - Floor[(n - i + 1)/2]), {i, n}], {n, 70}]
%t A237669 Table[Count[Flatten[IntegerPartitions[3 n,{3}]],_?PrimeQ],{n,60}] (* _Harvey P. Dale_, Oct 16 2016 *)
%Y A237669 Cf. A010051, A019298, A236364, A236370, A236758, A236762, A237264.
%K A237669 nonn,easy
%O A237669 1,2
%A A237669 _Wesley Ivan Hurt_, Feb 11 2014