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A054979
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e-perfect numbers: numbers n such that the sum of the e-divisors (exponential divisors) of n equals 2n.
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10
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36, 180, 252, 396, 468, 612, 684, 828, 1044, 1116, 1260, 1332, 1476, 1548, 1692, 1800, 1908, 1980, 2124, 2196, 2340, 2412, 2556, 2628, 2700, 2772, 2844, 2988, 3060, 3204, 3276, 3420, 3492, 3636, 3708, 3852, 3924, 4068, 4140, 4284, 4572, 4716
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The e-divisors (or exponential divisors) of x=Product p(i)^r(i) are all numbers of the form Product p(i)^s(i) where s(i) divides r(i) for all i.
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REFERENCES
| R. K. Guy, Unsolved Problems In Number Theory, B17.
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LINKS
| Eric Weisstein's World of Mathematics, e-Perfect Number
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EXAMPLE
| The e-divisors of 36 are 2*3, 4*3, 2*9 and 4*9 and the sum of these = 2*36, so 36 is e-perfect.
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PROG
| (PARI) is(n)=my(f=factor(n)); prod(i=1, #f[, 1], sumdiv(f[i, 2], d, f[i, 1]^d))==2*n \\ Charles R Greathouse IV, Nov 22 2011
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CROSSREFS
| Cf. A051377, A054980.
Sequence in context: A017054 A166708 A127657 * A102949 A017138 A120465
Adjacent sequences: A054976 A054977 A054978 * A054980 A054981 A054982
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KEYWORD
| nonn
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), May 29 2000
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