This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A083397 Largest prime factor of n! + k where k is the least positive integer such that n! + k is a square. 0
 0, 2, 3, 5, 11, 3, 71, 67, 67, 127, 13, 509, 137, 37, 71471, 71471, 409993, 941351, 24419, 287093, 7147792819, 110647261, 80392811773, 4716679469, 4716679469, 323905128133, 8392290961, 551615338229, 34178276390953, 73669621631 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n > 1, n! cannot be a perfect square. Proof: All exponents of the prime factors of a square are even. But in the factorization of n! at least one of the primes will appear only once due to Bertrand's Postulate which says there is always a prime between m and 2m. LINKS EXAMPLE a(9)=67 because 9!+729 = 363609 = 3^4*67^2 is a square with largest prime factor of 67. MATHEMATICA Join[{0}, Table[FactorInteger[(Floor[Sqrt[n!]]+1)^2][[-1, 1]], {n, 2, 30}]] (* Harvey P. Dale, Jan 04 2012 *) CROSSREFS Cf. A068869. Sequence in context: A197312 A259387 A130165 * A067362 A248793 A131200 Adjacent sequences:  A083394 A083395 A083396 * A083398 A083399 A083400 KEYWORD easy,nonn AUTHOR Jason Earls, Jun 06 2003 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.

Last modified May 19 15:24 EDT 2019. Contains 323395 sequences. (Running on oeis4.)