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 A363528 #8 Jun 11 2023 11:18:31
%S A363528 1,1,1,1,1,1,1,1,1,1,1,2,1,1,3,1,1,3,1,2,6,2,3,9,3,4,11,4,5,16,6,8,24,
%T A363528 8,10,31,11,14,41,18,18,59,21,27,74,30,32,100,35,43,128,54,53,173,58,
%U A363528 78,215,81,88,294,97,123,362,150,146,469,162,221,577
%N A363528 Number of strict integer partitions of n with weighted sum divisible by reverse-weighted sum.
%C A363528 The (one-based) weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i*y_i. This is also the sum of partial sums of the reverse.
%e A363528 The a(n) partitions for n = 1, 12, 15, 21, 24, 26:
%e A363528 (1) (12) (15) (21) (24) (26)
%e A363528 (9,2,1) (11,3,1) (15,5,1) (17,6,1) (11,8,4,2,1)
%e A363528 (9,3,2,1) (16,3,2) (18,4,2) (12,6,5,2,1)
%e A363528 (11,7,2,1) (12,9,2,1) (13,5,4,3,1)
%e A363528 (12,5,3,1) (13,7,3,1)
%e A363528 (10,5,3,2,1) (14,5,4,1)
%e A363528 (15,4,3,2)
%e A363528 (10,8,3,2,1)
%e A363528 (11,6,4,2,1)
%t A363528 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Divisible[Total[Accumulate[#]],Total[Accumulate[Reverse[#]]]]&]],{n,30}]
%Y A363528 The non-strict version is A363525.
%Y A363528 A000041 counts integer partitions, strict A000009.
%Y A363528 A264034 counts partitions by weighted sum, reverse A358194.
%Y A363528 A304818 gives weighted sum of prime indices, row-sums of A359361.
%Y A363528 A318283 gives weighted sum of reversed prime indices, row-sums of A358136.
%Y A363528 A320387 counts multisets by weighted sum, zero-based A359678.
%Y A363528 A363526 counts partitions with weighted sum 3n, reverse A363531.
%Y A363528 Cf. A008284, A053632, A067538, A222855, A222970, A358137, A359754, A359755, A362558, A362559, A362560.
%K A363528 nonn
%O A363528 1,12
%A A363528 _Gus Wiseman_, Jun 10 2023