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A129575
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Exponential abundant numbers: integers n for which A126164(n)>n, or equivalently for which A051377(n)>2n.
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0
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900, 1764, 3600, 4356, 4500, 4900, 6084, 6300, 7056, 8100, 8820, 9900, 10404, 11700, 12348, 12996, 14700, 15300, 17100, 19044, 19404, 20700, 21780, 22500, 22932, 25200, 26100, 27900, 29988, 30276, 30420, 30492, 31500, 33300, 33516, 34596
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OFFSET
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1,1
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COMMENTS
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There are only 52189 exponential abundant numbers less than 50 million, which suggests that these account for approximately 0.1% of all integers.
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REFERENCES
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Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350.
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LINKS
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Table of n, a(n) for n=1..36.
Eric Weisstein's World of Mathematics, e-Divisor.
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EXAMPLE
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The third integer that is exceeded by its proper exponential divisor sum is 3600. Hence a(3)=3600.
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MATHEMATICA
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ExponentialDivisors[1]={1}; ExponentialDivisors[n_]:=Module[{}, {pr, pows}=Transpose@FactorInteger[n]; divpowers=Distribute[Divisors[pows], List]; Sort[Times@@(pr^Transpose[divpowers])]]; properexponentialdivisorsum[k_]:=Plus@@ExponentialDivisors[k]-k; Select[Range[5 10^4], properexponentialdivisorsum[ # ]># &]
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CROSSREFS
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Cf. A126164, A051377, A049419, A054979, A054980.
Sequence in context: A061044 A127658 A137490 * A074853 A162143 A069096
Adjacent sequences: A129572 A129573 A129574 * A129576 A129577 A129578
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KEYWORD
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easy,nonn
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AUTHOR
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Ant King, Apr 28 2007
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STATUS
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approved
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