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A335288
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Unitary balanced numbers: numbers k such that uphi(k) (A047994) divides usigma(k) (A034448).
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2
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1, 2, 3, 6, 14, 15, 30, 35, 42, 44, 60, 70, 78, 105, 126, 132, 190, 210, 220, 312, 357, 418, 558, 570, 660, 693, 714, 728, 910, 1045, 1254, 1386, 1395, 1428, 1540, 2090, 2108, 2184, 2730, 2790, 3135, 3465, 3640, 3692, 3762, 4522, 4620, 4674, 5236, 5278, 6270
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OFFSET
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1,2
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COMMENTS
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Terms that are also balanced numbers (A020492) include the squarefree balanced numbers (A078557). The nonsquarefree common terms are in A335289.
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LINKS
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EXAMPLE
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6 is a term since usigma(6) = 12 is divisible by uphi(6) = 2.
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MATHEMATICA
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f[1, 1] = 1; f[p_, e_]:= (p^e + 1)/(p^e -1); ubalQ[n_] := IntegerQ[Times @@ (f @@@ FactorInteger[n])]; Select[Range[10^4], ubalQ]
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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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