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 A129575 Exponential abundant numbers: integers n for which A126164(n)>n, or equivalently for which A051377(n)>2n. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are only 52189 exponential abundant numbers less than 50 million, which suggests that these account for approximately 0.1% of all integers. REFERENCES Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350. LINKS Eric Weisstein's World of Mathematics, e-Divisor. EXAMPLE The third integer that is exceeded by its proper exponential divisor sum is 3600. Hence a(3)=3600. MATHEMATICA 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[ # ]># &] CROSSREFS Cf. A126164, A051377, A049419, A054979, A054980. Sequence in context: A061044 A127658 A137490 * A074853 A162143 A069096 Adjacent sequences:  A129572 A129573 A129574 * A129576 A129577 A129578 KEYWORD easy,nonn AUTHOR Ant King, Apr 28 2007 STATUS approved

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