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 A352874 #7 May 15 2022 11:50:37
%S A352874 3,5,7,9,11,13,15,17,18,19,21,23,25,27,29,30,31,33,35,37,39,41,42,43,
%T A352874 45,47,49,50,51,53,54,55,57,59,61,63,65,66,67,69,70,71,73,75,77,78,79,
%U A352874 81,83,85,87,89,90,91,93,95,97,98,99,101,102,103,105,107,109
%N A352874 Heinz numbers of integer partitions with positive crank, counted by A001522.
%C A352874 The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%C A352874 The crank of a partition p is defined to be (i) the largest part of p if there is no 1 in p and (ii) (the number of parts larger than the number of 1's) minus (the number of 1's). [Definition copied from A342192; see A064428 for a different wording.]
%F A352874 Complement of A342192 in A352873.
%e A352874 The terms together with their prime indices begin:
%e A352874 3: (2) 30: (3,2,1) 54: (2,2,2,1)
%e A352874 5: (3) 31: (11) 55: (5,3)
%e A352874 7: (4) 33: (5,2) 57: (8,2)
%e A352874 9: (2,2) 35: (4,3) 59: (17)
%e A352874 11: (5) 37: (12) 61: (18)
%e A352874 13: (6) 39: (6,2) 63: (4,2,2)
%e A352874 15: (3,2) 41: (13) 65: (6,3)
%e A352874 17: (7) 42: (4,2,1) 66: (5,2,1)
%e A352874 18: (2,2,1) 43: (14) 67: (19)
%e A352874 19: (8) 45: (3,2,2) 69: (9,2)
%e A352874 21: (4,2) 47: (15) 70: (4,3,1)
%e A352874 23: (9) 49: (4,4) 71: (20)
%e A352874 25: (3,3) 50: (3,3,1) 73: (21)
%e A352874 27: (2,2,2) 51: (7,2) 75: (3,3,2)
%e A352874 29: (10) 53: (16) 77: (5,4)
%t A352874 ck[y_]:=With[{w=Count[y,1]},If[w==0,Max@@y,Count[y,_?(#>w&)]-w]];
%t A352874 Select[Range[100],ck[Reverse[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]]>0&]
%Y A352874 * = unproved
%Y A352874 These partitions are counted by A001522.
%Y A352874 The case of zero crank is A342192, counted by A064410.
%Y A352874 The case of nonnegative crank is A352873, counted by A064428.
%Y A352874 A000700 counts self-conjugate partitions, ranked by A088902.
%Y A352874 A001222 counts prime indices, distinct A001221.
%Y A352874 *A001522 counts partitions with a fixed point, ranked by A352827.
%Y A352874 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A352874 *A064428 counts partitions without a fixed point, ranked by A352826.
%Y A352874 A115720 and A115994 count partitions by their Durfee square.
%Y A352874 A122111 represents partition conjugation using Heinz numbers.
%Y A352874 A238395 counts reversed partitions with a fixed point, ranked by A352872.
%Y A352874 Cf. A065770, A093641, A118199, A188674, A252464, A257990, A325163, A325169, A344609, A352828, A352831.
%K A352874 nonn
%O A352874 1,1
%A A352874 _Gus Wiseman_, Apr 09 2022