The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A291566

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A291566

Non-primitive balanced numbers: balanced numbers of the form m*n where m, n > 1 are both balanced.
(history; published version)

#15 by Alois P. Heinz at Wed Jun 26 08:11:38 EDT 2019

STATUS

proposed

approved

#14 by Amiram Eldar at Wed Jun 26 07:05:51 EDT 2019

STATUS

editing

proposed

#13 by Amiram Eldar at Wed Jun 26 06:17:13 EDT 2019

LINKS

Amiram Eldar, <a href="/A291566/b291566.txt">Table of n, a(n) for n = 1..5000</a>

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 *)

STATUS

approved

editing

#12 by Joerg Arndt at Wed Sep 06 03:51:38 EDT 2017

STATUS

proposed

approved

#11 by Charles R Greathouse IV at Tue Sep 05 15:42:58 EDT 2017

STATUS

editing

proposed

Discussion

Tue Sep 05

15:43

Charles R Greathouse IV: Clarified the name.

#10 by Charles R Greathouse IV at Tue Sep 05 15:42:55 EDT 2017

NAME

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

COMMENTS

A positive integer, n, is a balanced number (A020492) if sigma(n) is a multiple of phi(n). Since Phi phi and Sigma 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.

This sequence eliminates these "non-primitive" terms.

STATUS

approved

editing

#9 by N. J. A. Sloane at Mon Sep 04 20:57:13 EDT 2017

STATUS

reviewed

approved

#8 by Jud McCranie at Sun Aug 27 18:34:18 EDT 2017

STATUS

proposed

reviewed

#7 by Michel Marcus at Sun Aug 27 11:26:22 EDT 2017

STATUS

editing

proposed

Discussion

Sun Aug 27

18:34

Jud McCranie: I wasn't able to use it.

#6 by Michel Marcus at Sun Aug 27 11:26:18 EDT 2017

CROSSREFS

Cf. A020492, A291563A291565.

STATUS

proposed

editing