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A291566 Non-primitive balanced numbers: balanced numbers of the form m*n where m, n > 1 are both balanced. 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A175907 A114649 A090126 * A326580 A070195 A241190
KEYWORD
nonn
AUTHOR
Jud McCranie, Aug 26 2017
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)