A055489 Largest number x such that sum of divisors of x is n!.

5, 23, 95, 719, 5039, 39917, 361657, 3624941, 39904153, 479001599, 6226862869, 87178291199, 1307672080867, 20922780738961, 355687390376431, 6402373545694717, 121645099711277873, 2432902005056589697, 51090942157413850441

Offset: 3

Author

Labos Elemer, Jun 28 2000

Keywords

• nonn

Comments

For n = 1, a(1) = 1; for n = 2 there is no solution.

For n in A002982, a(n) = n!-1.

Examples

			For n = 6, the 15 solutions are as follows: {264, 270, 280, 354, 376, 406, 418, 435, 459, 478, 537, 623, 649, 667, 719}.
		

References

• R. K. Guy (1981): Unsolved Problems In Number Theory, B39.

Links

• 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.

Crossrefs

Cf. A000203, A000142, A002982, A055486, A055488, A057637.

Programs

PARI

a(n) = {fn = n!; x = fn - 1; while(sigma(x) != fn, x--); x;} \\ Michel Marcus, Dec 17 2013

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

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