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A005231
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Odd abundant numbers (odd numbers n whose sum of divisors exceeds 2n).
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21
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945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 7875, 8085, 8415, 8505, 8925, 9135, 9555, 9765, 10395, 11025, 11655, 12285, 12705, 12915, 13545, 14175, 14805, 15015, 15435, 16065, 16695, 17325, 17955
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| While the first even abundant number is 12 = 2^2*3, the first odd abundant is 945 = 3^3*5*7, the 232nd abundant number.
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REFERENCES
| W. Dunham, Euler: The Master of Us All, The Mathematical Association of America Inc., Washington, D.C., 1999, p. 13.
R. K. Guy, Unsolved Problems in Number Theory, B2.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Jill Britton, Perfect Number Analyzer.
L. E. Dickson, Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors, American Journal of Mathematics 35 (1913), pp. 413-422.
Walter Nissen, Abundancy : Some Resources
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MAPLE
| A005231 := proc(n) option remember ; local a ; if n = 1 then 945 ; else for a from procname(n-1)+2 by 2 do if numtheory[sigma](a) > 2*a then return a; end if; end do: end if; end proc: # R. J. Mathar, Mar 20 2011
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MATHEMATICA
| fQ[n_] := DivisorSigma[1, n] > 2n; Select[1 + 2Range@ 9000, fQ] (* Robert G. Wilson v, Mar 20 2011 *)
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PROG
| (PARI) je=[ ]; forstep(n=1, 15000, 2, x=sigma(n); if(x>(2*n), je=concat(je, n))); je
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CROSSREFS
| Cf. A006038, A115414, A064001, A112640, A122036, A136446, A005101, A173490, A039725.
Sequence in context: A133814 A104438 A125013 * A174865 A174535 A006038
Adjacent sequences: A005228 A005229 A005230 * A005232 A005233 A005234
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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