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 A367588 #13 Feb 04 2024 21:22:28
%S A367588 0,0,0,1,1,2,3,3,4,5,6,5,9,6,9,10,11,8,15,9,16,14,15,11,23,14,18,18,
%T A367588 23,14,30,15,26,22,24,22,38,18,27,26,38,20,42,21,37,36,33,23,53,27,42,
%U A367588 34,44,26,54,34,53,38,42,29,74,30,45,49,57,40,66,33,58,46
%N A367588 Number of integer partitions of n with exactly two distinct parts, both appearing with the same multiplicity.
%C A367588 The Heinz numbers of these partitions are given by A268390.
%H A367588 Alois P. Heinz, <a href="/A367588/b367588.txt">Table of n, a(n) for n = 0..10000</a>
%F A367588 G.f.: Sum_{i, j>0} x^(j*(2*i+1))/(1-x^j). - _John Tyler Rascoe_, Feb 04 2024
%e A367588 The a(3) = 1 through a(12) = 9 partitions (A = 10, B = 11):
%e A367588 (21) (31) (32) (42) (43) (53) (54) (64) (65) (75)
%e A367588 (41) (51) (52) (62) (63) (73) (74) (84)
%e A367588 (2211) (61) (71) (72) (82) (83) (93)
%e A367588 (3311) (81) (91) (92) (A2)
%e A367588 (222111) (3322) (A1) (B1)
%e A367588 (4411) (4422)
%e A367588 (5511)
%e A367588 (333111)
%e A367588 (22221111)
%t A367588 Table[Sum[Floor[(d-1)/2],{d,Divisors[n]}],{n,30}]
%Y A367588 For any multiplicities we have A002133, ranks A007774.
%Y A367588 For any number of distinct parts we have A047966, ranks A072774.
%Y A367588 For distinct multiplicities we have A182473, ranks A367589.
%Y A367588 These partitions have ranks A268390.
%Y A367588 A000041 counts integer partitions, strict A000009.
%Y A367588 A072233 counts partitions by number of parts.
%Y A367588 A116608 counts partitions by number of distinct parts.
%Y A367588 Cf. A023645, A091602, A116861, A181819, A243978, A367582.
%K A367588 nonn
%O A367588 0,6
%A A367588 _Gus Wiseman_, Dec 01 2023