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 A359906 #6 Jan 22 2023 09:15:15
%S A359906 1,2,2,4,2,8,2,10,9,14,2,39,2,24,51,49,2,109,2,170,144,69,2,455,194,
%T A359906 116,381,668,2,1378,2,985,956,316,2043,4328,2,511,2293,6656,2,8634,2,
%U A359906 8062,14671,1280,2,26228,8035,15991,11614,25055,2,47201,39810,65092
%N A359906 Number of integer partitions of n with integer mean and integer median.
%C A359906 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%e A359906 The a(1) = 1 through a(9) = 9 partitions:
%e A359906 1 2 3 4 5 6 7 8 9
%e A359906 11 111 22 11111 33 1111111 44 333
%e A359906 31 42 53 432
%e A359906 1111 51 62 441
%e A359906 222 71 522
%e A359906 321 2222 531
%e A359906 411 3221 621
%e A359906 111111 3311 711
%e A359906 5111 111111111
%e A359906 11111111
%t A359906 Table[Length[Select[IntegerPartitions[n], IntegerQ[Mean[#]]&&IntegerQ[Median[#]]&]],{n,1,30}]
%Y A359906 For just integer mean we have A067538, strict A102627, ranked by A316413.
%Y A359906 For just integer median we have A325347, strict A359907, ranked by A359908.
%Y A359906 These partitions are ranked by A360009.
%Y A359906 A000041 counts partitions, strict A000009.
%Y A359906 A058398 counts partitions by mean, see also A008284, A327482.
%Y A359906 A051293 counts subsets with integer mean, median A000975.
%Y A359906 A326567/A326568 gives mean of prime indices.
%Y A359906 A326622 counts factorizations with integer mean, strict A328966.
%Y A359906 A359893/A359901/A359902 count partitions by median.
%Y A359906 A360005(n)/2 gives median of prime indices.
%Y A359906 Cf. A000016, A082550, A237984, A240219, A326669, A327475, A349156, A359894, A359897, A359905.
%K A359906 nonn
%O A359906 1,2
%A A359906 _Gus Wiseman_, Jan 21 2023