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A068403
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Numbers k such that sigma(k) > 3*k.
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21
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180, 240, 360, 420, 480, 504, 540, 600, 660, 720, 780, 840, 900, 960, 1008, 1080, 1200, 1260, 1320, 1344, 1440, 1512, 1560, 1584, 1620, 1680, 1800, 1848, 1872, 1890, 1920, 1980, 2016, 2040, 2100, 2160, 2184, 2280, 2340, 2352, 2376, 2400, 2520, 2640
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OFFSET
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1,1
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COMMENTS
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Davenport shows that these numbers have positive density. Are there good bounds for the density?
G. Miller & M. Whalen suggested that 1018976683725 (3^3*5^2*7^2*11*13*17*19*23*29) might be the smallest odd number in the sequence (a fact now, see A119240 and A023197). - Michel Marcus, May 01 2013
Behrend (1933) found the bounds (0.009, 0.110) for the asymptotic density.
Wall et al. (1972) found the bounds (0.0186, 0.0461).
The upper bound was reduced to 0.0214614 using Deléglise's method by McDaniel College (2010). (End)
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REFERENCES
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Harold Davenport, Über numeri abundantes, Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl., No. 6 (1933), pp. 830-837.
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LINKS
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Gordon L. Miller and Mary T. Whalen, Multiply Abundant Numbers, School Science and Mathematics, Volume 95, Issue 5 (May 1995), pp. 256-259.
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FORMULA
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MAPLE
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MATHEMATICA
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Select[Range[3000], DivisorSigma[1, #]>3#&] (* Harvey P. Dale, Aug 12 2023 *)
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PROG
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(PARI) for(n=1, 3000, if(sigma(n)>3*n, print1(n, ", "))) \\ Indranil Ghosh, Apr 10 2017
(Python)
from sympy import divisor_sigma
print([n for n in range(180, 3001) if divisor_sigma(n)>3*n]) # Indranil Ghosh, Apr 10 2017
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CROSSREFS
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Terms not divisible by 6 are in A126104.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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