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A153501
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Abundant numbers n such that n/(sigma(n)-2n) is an integer.
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12
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12, 18, 20, 24, 40, 56, 88, 104, 120, 196, 224, 234, 368, 464, 650, 672, 992, 1504, 1888, 1952, 3724, 5624, 9112, 11096, 13736, 15376, 15872, 16256, 17816, 24448, 28544, 30592, 32128, 77744, 98048, 122624, 128768, 130304, 174592, 396896, 507392
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OFFSET
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1,1
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COMMENTS
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Sigma(n)-2n is the abundance of n.
The only odd term in this sequence < 2*10^12 is 173369889. - Donovan Johnson, Feb 15 2012
Equivalently, the abundancy of n, ab=sigma(n)/n, satisfies the following relation: numerator(ab) = 2*denominator(ab)+1, that is, ab=(2k+1)/k where k is the integer ratio mentioned in definition. - Michel Marcus, Nov 07 2014
The tri-perfect numbers (A005820) are in this sequence, since their abundancy is 3n/n = 3 = (2k+1)/k with k=1. - Michel Marcus, Nov 07 2014
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LINKS
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EXAMPLE
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The abundance of 174592 = sigma(174592)-2*174592 = 43648. 174592/43648 = 4.
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MAPLE
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filter:= proc(n) local s; s:= numtheory:-sigma(n); (s > 2*n) and (n mod (s-2*n) = 0) end proc:
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MATHEMATICA
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filterQ[n_] := Module[{s = DivisorSigma[1, n]}, s > 2n && Mod[n, s - 2n] == 0];
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PROG
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(PARI) isok(n) = ((ab = (sigma(n)-2*n))>0) && (n % ab == 0) \\ Michel Marcus, Jul 16 2013
(Sage)
t = sigma(n, 1) - 2*n
return t > 0 and t.divides(n)
return filter(is_A153501, range(1, len))
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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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