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

3,1

Comments

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

References

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

Links

Table of n, a(n) for n=3..22.

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

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}

Crossrefs

Cf. A000203, A000142, A055486, A055487, A055489

Sequence in context: A146746 A073541 A268887 * A177049 A127922 A262247

Adjacent sequences: A055485 A055486 A055487 * A055489 A055490 A055491

Keyword

nonn

Author

Labos Elemer, Jun 28 2000

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

Status

approved