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 A339452 #10 Feb 16 2025 08:34:01
%S A339452 1,1,1,1,3,1,7,1,1,5,1,1,9,7,3,1,3,1,7,11,13,1,7,1,11,35,25,31,27,5,
%T A339452 157,1,31,131,39,31,33,37,183,179,135,157,7,265,3,871,187,865,259,879,
%U A339452 867,179,1593,6073,1593,271,5995,149,6661,2411,1509,997,1045,5887
%N A339452 Number of compositions (ordered partitions) of n into distinct parts such that the geometric mean of the parts is an integer.
%H A339452 Eric W. Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeometricMean.html">Geometric Mean</a>
%H A339452 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%e A339452 a(10) = 5 because we have [10], [9, 1], [1, 9], [8, 2] and [2, 8].
%t A339452 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@#&&IntegerQ[GeometricMean[#]]&]],{n,0,15}] (* _Gus Wiseman_, Oct 30 2022 *)
%Y A339452 For partitions we have A326625, non-strict A067539 (ranked by A326623).
%Y A339452 The version for subsets is A326027.
%Y A339452 For arithmetic mean we have A339175, non-strict A271654.
%Y A339452 The non-strict case is counted by A357710, ranked by A357490.
%Y A339452 A032020 counts strict compositions.
%Y A339452 A067538 counts partitions with integer average.
%Y A339452 A078175 lists numbers whose prime factors have integer average.
%Y A339452 A320322 counts partitions whose product is a perfect power.
%Y A339452 Cf. A051293, A078174, A096199, A102627, A326622, A326624, A326028, A326641, A326645, A335405.
%K A339452 nonn
%O A339452 1,5
%A A339452 _Ilya Gutkovskiy_, Dec 05 2020