OFFSET
1,1
COMMENTS
A positive integer, n, is a balanced number (A020492) if sigma(n) is a multiple of phi(n). Since phi and sigma are multiplicative functions, if m and n are balanced numbers and gcd(m,n)=1, mn is also a balanced number. This sequence consists of only these imprimitive terms.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..5000
EXAMPLE
2 and 3 are balanced numbers, gcd(2,3)=1, so 6 is a non-primitive balanced number.
MATHEMATICA
balQ[n_] := Divisible[DivisorSigma[1, n], EulerPhi[n]]; nonprimQ[n_] := balQ[n] && Module[{d = Divisors[n], ans = False}, Do[If[GCD[d[[k]], n/d[[k]]]==1 && balQ[ d[[k]]] && balQ[n/d[[k]]], ans=True; Break[]], {k, 2, Floor[Length[d]/2]}]; ans]; Select[Range[50000], nonprimQ] (* Amiram Eldar, Jun 26 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jud McCranie, Aug 26 2017
STATUS
approved