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 A340787 #13 Apr 09 2021 09:41:15 %S A340787 3,5,7,10,11,13,14,15,17,19,21,22,23,25,26,28,29,31,33,34,35,37,38,39, %T A340787 41,42,43,44,46,47,49,51,52,53,55,57,58,59,61,62,63,65,66,67,68,69,70, %U A340787 71,73,74,76,77,78,79,82,83,85,86,87,88,89,91,92,93,94,95 %N A340787 Heinz numbers of integer partitions of positive rank. %C A340787 The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions. %C A340787 The Dyson rank of a nonempty partition is its maximum part minus its length. The rank of an empty partition is undefined. %H A340787 Freeman J. Dyson, <a href="https://doi.org/10.1016/S0021-9800(69)80006-2">A new symmetry of partitions</a>, Journal of Combinatorial Theory 7.1 (1969): 56-61. %H A340787 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000145">St000145: The Dyson rank of a partition</a> %F A340787 For all terms A061395(a(n)) > A001222(a(n)). %e A340787 The sequence of partitions together with their Heinz numbers begins: %e A340787 3: (2) 28: (4,1,1) 49: (4,4) 69: (9,2) %e A340787 5: (3) 29: (10) 51: (7,2) 70: (4,3,1) %e A340787 7: (4) 31: (11) 52: (6,1,1) 71: (20) %e A340787 10: (3,1) 33: (5,2) 53: (16) 73: (21) %e A340787 11: (5) 34: (7,1) 55: (5,3) 74: (12,1) %e A340787 13: (6) 35: (4,3) 57: (8,2) 76: (8,1,1) %e A340787 14: (4,1) 37: (12) 58: (10,1) 77: (5,4) %e A340787 15: (3,2) 38: (8,1) 59: (17) 78: (6,2,1) %e A340787 17: (7) 39: (6,2) 61: (18) 79: (22) %e A340787 19: (8) 41: (13) 62: (11,1) 82: (13,1) %e A340787 21: (4,2) 42: (4,2,1) 63: (4,2,2) 83: (23) %e A340787 22: (5,1) 43: (14) 65: (6,3) 85: (7,3) %e A340787 23: (9) 44: (5,1,1) 66: (5,2,1) 86: (14,1) %e A340787 25: (3,3) 46: (9,1) 67: (19) 87: (10,2) %e A340787 26: (6,1) 47: (15) 68: (7,1,1) 88: (5,1,1,1) %t A340787 Select[Range[2,100],PrimePi[FactorInteger[#][[-1,1]]]>PrimeOmega[#]&] %Y A340787 Note: A-numbers of Heinz-number sequences are in parentheses below. %Y A340787 These partitions are counted by A064173. %Y A340787 The odd case is A101707 (A340604). %Y A340787 The even case is A101708 (A340605). %Y A340787 The negative version is (A340788). %Y A340787 A001222 counts prime factors. %Y A340787 A061395 selects the maximum prime index. %Y A340787 A072233 counts partitions by sum and length. %Y A340787 A168659 = partitions whose greatest part divides their length (A340609). %Y A340787 A168659 = partitions whose length divides their greatest part (A340610). %Y A340787 A200750 = partitions whose length and maximum are relatively prime. %Y A340787 - Rank - %Y A340787 A047993 counts partitions of rank 0 (A106529). %Y A340787 A063995/A105806 count partitions by Dyson rank. %Y A340787 A064174 counts partitions of nonnegative/nonpositive rank (A324562/A324521). %Y A340787 A101198 counts partitions of rank 1 (A325233). %Y A340787 A257541 gives the rank of the partition with Heinz number n. %Y A340787 A324520 counts partitions with rank equal to least part (A324519). %Y A340787 A340601 counts partitions of even rank (A340602), with strict case A117192. %Y A340787 A340692 counts partitions of odd rank (A340603), with strict case A117193. %Y A340787 Cf. A003114, A006141, A039900, A056239, A096401, A112798, A117409, A316413, A324517, A325134, A326845, A340828. %K A340787 nonn %O A340787 1,1 %A A340787 _Gus Wiseman_, Jan 29 2021