A291566 Non-primitive balanced numbers: balanced numbers of the form m*n where m, n > 1 are both balanced.

6, 30, 42, 70, 105, 168, 210, 420, 570, 714, 744, 840, 1254, 1848, 2090, 2436, 2730, 2970, 3135, 3720, 5016, 6270, 6678, 8680, 9240, 10098, 10788, 11868, 12180, 12192, 12540, 13566, 14630, 15834, 16188, 20790, 21318, 24024, 24882, 25080, 25908, 26040, 26796, 32130, 43890, 48360

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

Cf. A020492, A291565.

Sequence in context: A175907 A114649 A090126 * A326580 A070195 A241190

Adjacent sequences: A291563 A291564 A291565 * A291567 A291568 A291569

Keyword

nonn

Author

Jud McCranie, Aug 26 2017

Status

approved