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A308045
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Numbers k such that usigma(k) = round(zeta(2)/zeta(3)*k), where usigma(k) is the sum of unitary divisors of k (A034448).
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0
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1, 2, 3, 4, 35, 44, 111, 123, 1105, 1900, 2920, 12452, 17889, 34200, 65067, 716148, 14134055, 179040201, 221709100, 221743300, 221766100, 221788900, 1120968741, 1272582040, 1441454511, 7339101375
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OFFSET
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1,2
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COMMENTS
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zeta(2)/zeta(3) is the asymptotic mean of the unitary abundancy index usigma(k)/k (A306633).
a(27) > 10^10.
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LINKS
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EXAMPLE
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35 is in the sequence since usigma(35) = 48, and (zeta(2)/zeta(3)) * 35 = 47.895... has a round value of 48.
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MATHEMATICA
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usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); meanAb = Zeta[2]/Zeta[3]; Select[Range[10^6], usigma[#] == Round[meanAb*#] &]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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