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 A360070 #18 Jan 29 2023 21:02:11
%S A360070 1,4,8,9,12,16,18,20,25,27,32,36,45,48,49,50,54,63,64,72,75,80,81,90,
%T A360070 96,98,99,100,108,112,117,121,125,128,144,147,150,160,162,169,175,176,
%U A360070 180,192,196,200,208,216,224,225,240,242,243,245,250,252,256,272
%N A360070 Numbers for which there exists an integer partition such that the parts have the same mean as the multiplicities.
%C A360070 Conjecture: No term > 1 is squarefree.
%e A360070 A partition of 20 with the same mean as its multiplicities is (5,4,3,2,1,1,1,1,1,1), so 20 is in the sequence.
%t A360070 Select[Range[30],Select[IntegerPartitions[#],Mean[#]==Mean[Length/@Split[#]]&]!={}&]
%Y A360070 Positions of positive terms in A360068, ranked by A359903.
%Y A360070 A000041 counts partitions, strict A000009.
%Y A360070 A058398 counts partitions by mean, see also A008284, A327482.
%Y A360070 A088529/A088530 gives mean of prime signature (A124010).
%Y A360070 A326567/A326568 gives mean of prime indices (A112798).
%Y A360070 Cf. A005117, A067340, A067538, A240219, A316313, A349156, A359904, A359905, A360069.
%K A360070 nonn
%O A360070 1,2
%A A360070 _Gus Wiseman_, Jan 27 2023
%E A360070 a(22)-a(58) from _Alois P. Heinz_, Jan 29 2023