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A055489
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Largest number x such that sum of divisors of x is n!.
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5
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5, 23, 95, 719, 5039, 39917, 361657, 3624941, 39904153, 479001599, 6226862869, 87178291199, 1307672080867, 20922780738961, 355687390376431, 6402373545694717, 121645099711277873, 2432902005056589697, 51090942157413850441
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OFFSET
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3,1
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COMMENTS
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For n = 1, a(1) = 1; for n = 2 there is no solution.
For n in A002982, a(n) = n!-1.
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REFERENCES
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R. K. Guy (1981): Unsolved Problems In Number Theory, B39.
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LINKS
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Ray Chandler, Table of n, a(n) for n=3..52
Max A. Alekseyev, Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2.
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FORMULA
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a(n) = Max{x; Sigma[x] = n!} = Max{x; A000203(x) = A000142(n)}
a(n) = A057637(A000142(n)). - Ray Chandler, Jan 15 2009
a(A002982(n)) = A000142(A002982(n)) - 1. - Ray Chandler, Jan 15 2009
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EXAMPLE
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For n = 6, the 15 solutions are as follows: {264, 270, 280, 354, 376, 406, 418, 435, 459, 478, 537, 623, 649, 667, 719}.
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PROG
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(PARI) a(n) = {fn = n!; x = fn - 1; while(sigma(x) != fn, x--); x; } \\ Michel Marcus, Dec 17 2013
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CROSSREFS
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Cf. A000203, A000142, A002982, A055486, A055488, A057637.
Sequence in context: A028894 A254824 A140529 * A109765 A323922 A119012
Adjacent sequences: A055486 A055487 A055488 * A055490 A055491 A055492
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jun 28 2000
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EXTENSIONS
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More terms from Jud McCranie, Oct 09 2000
a(15) from Donovan Johnson, Aug 31 2008
a(16)-a(19) from Donovan Johnson, Nov 22 2008
a(20)-a(52) from Ray Chandler, Jan 15 2009
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STATUS
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approved
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