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A055489 Largest number x such that sum of divisors of x is n!. 5
5, 23, 95, 719, 5039, 39917, 361657, 3624941, 39904153, 479001599, 6226862869, 87178291199, 1307672080867, 20922780738961, 355687390376431, 6402373545694717, 121645099711277873, 2432902005056589697, 51090942157413850441 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
For n = 1, a(1) = 1; for n = 2 there is no solution.
For n in A002982, a(n) = n!-1.
REFERENCES
R. K. Guy (1981): Unsolved Problems In Number Theory, B39.
LINKS
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.
FORMULA
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
EXAMPLE
For n = 6, the 15 solutions are as follows: {264, 270, 280, 354, 376, 406, 418, 435, 459, 478, 537, 623, 649, 667, 719}.
PROG
(PARI) a(n) = {fn = n!; x = fn - 1; while(sigma(x) != fn, x--); x; } \\ Michel Marcus, Dec 17 2013
CROSSREFS
Sequence in context: A028894 A254824 A140529 * A109765 A323922 A368835
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 28 2000
EXTENSIONS
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
STATUS
approved

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)