A055488 Smallest number x such that sum of divisors of x is n!.

5, 14, 54, 264, 1560, 10920, 97440, 876960, 10263240, 112895640, 1348827480, 18029171160, 264370186080, 3806158356000, 62703141621120, 1128159304272000, 20422064875212000, 404757215566704000, 8208550091549808000, 177650747421074928000

Offset: 3

Author

Labos Elemer, Jun 28 2000

Keywords

• nonn

Comments

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

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

• 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, A055486, A055487, A055489

Formula

a(n) = Min{x; Sigma[x] = n!} = Min{x; A000203(x) = A000142(n)}

Extensions

More terms from Jud McCranie, Oct 09 2000

a(13), a(14) from Vim Wenders, Nov 06 2006, Jan 12 2007

a(15), a(16) from Donovan Johnson, Aug 26 2008, Mar 26 2010

a(17)-a(22) from Max Alekseyev, Jan 25 2012