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 A291565 #19 Mar 12 2021 05:50:06
%S A291565 1,2,3,12,14,15,35,56,78,140,190,248,264,270,357,418,594,616,630,812,
%T A291565 910,1045,1240,1485,1672,2214,2376,2580,3080,3339,3596,3828,3956,4064,
%U A291565 4180,4522,4674,5049,5278,5396,5544,5940,6426,7110,7668,8008,8636,8932,10659,11160,11880,12441,12648,15642
%N A291565 Primitive balanced numbers: primitive numbers not of the form m*n where m, n > 1 are both primitive.
%C A291565 A positive integer, n, is a balanced number (A020492) if sigma(n) is a multiple of phi(n). Since phi and sigma are multiplicative, if m and n are balanced numbers and gcd(m,n)=1, m*n is also a balanced number. This sequence eliminates these imprimitive terms.
%H A291565 Amiram Eldar, <a href="/A291565/b291565.txt">Table of n, a(n) for n = 1..10000</a>
%e A291565 2 and 3 are balanced numbers, gcd(2,3)=1, so 6 is a non-primitive balanced number; 2 and 3 are primitive balanced numbers.
%t A291565 balQ[n_] := Divisible[DivisorSigma[1,n], EulerPhi[n]]; primQ[n_] := balQ[n] && Module[{d = Divisors[n], ans = True}, Do[If[GCD[d[[k]], n/d[[k]]]==1 && balQ[ d[[k]]] && balQ[n/d[[k]]], ans=False; Break[]], {k, 2, Floor[Length[d]/2]}]; ans]; Select[Range[16000],primQ] (* _Amiram Eldar_, Jun 26 2019 *)
%Y A291565 Cf. A020492, A291566.
%K A291565 nonn
%O A291565 1,2
%A A291565 _Jud McCranie_, Aug 26 2017