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A291566
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Non-primitive balanced numbers: balanced numbers of the form m*n where m, n > 1 are both balanced.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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2 and 3 are balanced numbers, gcd(2,3)=1, so 6 is a non-primitive balanced number.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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