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A054377
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Primary pseudoperfect numbers.
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9
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OFFSET
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1,1
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COMMENTS
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Primary pseudoperfect numbers are the solutions of the "differential equation" n'=n-1, where n' is the arithmetic derivative of n. [From Paolo P. Lava, Nov 16 2009]
Hence a(n) is square-free, and is pseudoperfect if n > 1. Remarkably, a(n) has exactly n (distinct) prime factors for n < 9 (see Butske, Jaje, and Mayernik, 1999). - Jonathan Sondow, Apr 21 2013
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REFERENCES
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Butske, W.; Jaje, L.M.; and Mayernik, D.R, On the Equation $Sum_{p|N}1/p+1/N=1$, Pseudoperfect Numbers and Partially Weighted Graphs, Math. Comput., 69 (1999), 407-420.
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LINKS
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Table of n, a(n) for n=1..8.
J. Sondow and K. MacMillan, Reducing the Erdos-Moser equation 1^n + 2^n + . . . + k^n = (k+1)^n modulo k and k^2, Integers 11 (2011), #A34.
Eric Weisstein's World of Mathematics, Primary pseudoperfect number.
Wikipedia, Primary pseudoperfect number.
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CROSSREFS
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Cf. A005835, A007850, A168036, A190272, A191975, A203618, A216825, A216826.
Sequence in context: A123137 A014117 A188672 * A007018 A100016 A000610
Adjacent sequences: A054374 A054375 A054376 * A054378 A054379 A054380
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KEYWORD
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nonn,more,hard
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Title of Butske et al corrected by Jonathan Sondow, Apr 11 2012
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STATUS
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approved
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