login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

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

Cf. A000203, A000142, A055486, A055488.

Sequence in context: A028894 A254824 A140529 * A109765 A323922 A119012

Adjacent sequences:  A055486 A055487 A055488 * A055490 A055491 A055492

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 16:35 EDT 2021. Contains 345388 sequences. (Running on oeis4.)