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A005231 Odd abundant numbers (odd numbers n whose sum of divisors exceeds 2n). 25
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; text; internal format)
OFFSET

1,1

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.

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.

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

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

MATHEMATICA

fQ[n_] := DivisorSigma[1, n] > 2n; Select[1 + 2Range@ 9000, fQ] (* Robert G. Wilson v, Mar 20 2011 *)

PROG

(PARI) je=[ ]; forstep(n=1, 15000, 2, x=sigma(n); if(x>(2*n), je=concat(je, n))); je

CROSSREFS

Cf. A006038, A115414, A064001, A112640, A122036, A136446, A005101, A173490, A039725.

Sequence in context: A125013 A252192 A252185 * A174865 A174535 A243104

Adjacent sequences:  A005228 A005229 A005230 * A005232 A005233 A005234

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers

STATUS

approved

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Last modified March 2 23:56 EST 2015. Contains 255145 sequences.