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 A333636 #20 May 29 2020 15:42:47
%S A333636 0,0,0,2,0,2,3,2,3,3,5,3,3,2,5,5,7,5,7,5,5,5,11,7,7,7,11,7,13,7,13,7,
%T A333636 11,11,17,11,7,11,17,11,19,13,13,13,17,13,19,13,19,13,23,17,23,17,19,
%U A333636 17,17,17,29,19,19,17,23,19,29,19,31,19,29,19,31,19,31,23,29,23,37,19,37,23,29,23,41
%N A333636 a(n) is the greatest least part of a partition of n into prime parts which does not divide n, or 0 if no such prime exists.
%C A333636 For n = 2,3,4,6 a(n) = 0. For n > 6 there are no terms a(n) = 0, and therefore n has at least one prime partition whose least part prime does not divide n. This sequence lists the greatest such prime for each n. The indices of the records of this sequence are in A001043.
%e A333636 The only prime partition of 2 is [2], but 2|2, so a(2) = 0. Also, since [2,2,2] and [3,3] are the prime partitions of 6, with 2|6 and 3|6, a(6) = 0. The prime partitions of 5 are [2,3] and [5], but 2 does not divide 5 so a(5) = 2.
%e A333636 From _Michael De Vlieger_, Apr 01 2020: (Start)
%e A333636 Chart showing terms k in rows 5 <= n <= 24 of A333238, plotted at pi(k), with "." replacing terms k | n. In the table, we place a(n) in parenthesis:
%e A333636 n k
%e A333636 -------------------
%e A333636 5 (2) .
%e A333636 6 . .
%e A333636 7 (2) .
%e A333636 8 . (3)
%e A333636 9 (2) .
%e A333636 10 . (3) .
%e A333636 11 2 (3) .
%e A333636 12 . . (5)
%e A333636 13 2 (3) .
%e A333636 14 . (3) .
%e A333636 15 (2) . .
%e A333636 16 . 3 (5)
%e A333636 17 2 3 (5) .
%e A333636 18 . . 5 (7)
%e A333636 19 2 3 (5) .
%e A333636 20 . 3 . (7)
%e A333636 21 2 . (5) .
%e A333636 22 . 3 (5) .
%e A333636 23 2 3 (5) .
%e A333636 24 . . 5 7 (11)
%e A333636 ... (End)
%t A333636 Block[{m = 84, s, a}, a = ConstantArray[{}, m]; s = {Prime@ PrimePi@ m}; Do[If[# <= m, If[And[FreeQ[a[[#]], Last[s]], Mod[#, Last[s]] != 0], a = ReplacePart[a, # -> Union@ Append[a[[#]], Last@ s]], Nothing]; AppendTo[s, Last@ s], If[Last@ s == 2, s = DeleteCases[s, 2]; If[Length@ s == 0, Break[], s = MapAt[Prime[PrimePi[#] - 1] &, s, -1]], s = MapAt[Prime[PrimePi[#] - 1] &, s, -1]]] &@ Total[s], {i, Infinity}]; Map[If[Length[#] == 0, 0, Last@ #] &, Rest@ a]] (* _Michael De Vlieger_, Apr 01 2020 *)
%Y A333636 Cf. A001043, A331634, A333238, A333365.
%K A333636 nonn
%O A333636 2,4
%A A333636 _David James Sycamore_, Mar 30 2020