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 A326641 #7 Jul 16 2019 22:01:47
%S A326641 0,1,2,2,3,2,4,2,4,3,6,2,7,2,4,5,6,2,6,2,10,6,4,2,11,4,6,5,8,2,15,2,
%T A326641 10,6,6,8,16,2,4,8,20,2,17,2,8,17,4,2,27,9,20,8,14,2,21,10,35,10,6,2,
%U A326641 48,2,4,41,39,12,28,2,17,10,64,2,103,2,6,23
%N A326641 Number of integer partitions of n whose mean and geometric mean are both integers.
%C A326641 The Heinz numbers of these partitions are given by A326645.
%H A326641 Wikipedia, <a href="https://en.wikipedia.org/wiki/Geometric_mean">Geometric mean</a>
%e A326641 The a(4) = 3 through a(10) = 6 partitions (A = 10):
%e A326641 (4) (5) (6) (7) (8) (9) (A)
%e A326641 (22) (11111) (33) (1111111) (44) (333) (55)
%e A326641 (1111) (222) (2222) (111111111) (82)
%e A326641 (111111) (11111111) (91)
%e A326641 (22222)
%e A326641 (1111111111)
%t A326641 Table[Length[Select[IntegerPartitions[n],IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]],{n,0,30}]
%Y A326641 Partitions with integer mean are A067538.
%Y A326641 Partitions with integer geometric mean are A067539.
%Y A326641 Non-constant partitions with integer mean and geometric mean are A326642.
%Y A326641 Subsets with integer mean and geometric mean are A326643.
%Y A326641 Heinz numbers of partitions with integer mean and geometric mean are A326645.
%Y A326641 Strict partitions with integer mean and geometric mean are A326029.
%Y A326641 Cf. A051293, A078175, A082553, A102627, A316413, A326027, A326623, A326644, A326646, A326647.
%K A326641 nonn
%O A326641 0,3
%A A326641 _Gus Wiseman_, Jul 16 2019