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Search: id:A054980
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| A054980 |
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Primitive e-perfect numbers: sum of the e-divisors (exponential divisors) of n equals 2n. |
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+0
7
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| 36, 1800, 2700, 17424, 1306800, 4769856, 238492800, 357739200
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
The nonprimitive e-perfect numbers are obtained from the primitive ones by multiplying by m, if m is square-free and relatively prime to the primitive e-perfect number.
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REFERENCES
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R. K. Guy, Unsolved Problems In Number Theory, B17.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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Since 36=2^2*3^2 and divisors(2)={1,2}, all e-divisors are 2^1*3^1, 2^2*3^1, 2^1*3^2, and 2^2*3^2 or 6, 12, 18, 36, and these sum to 2*36, so 36 is e-perfect.
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CROSSREFS
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Cf. A051377, A054979.
Sequence in context: A095657 A034996 A113618 this_sequence A025754 A071128 A065782
Adjacent sequences: A054977 A054978 A054979 this_sequence A054981 A054982 A054983
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KEYWORD
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more,nonn
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AUTHOR
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Jud McCranie (j.mccranie(AT)comcast.net), May 29 2000
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