|
Search: id:A083397
|
|
|
| A083397 |
|
Largest prime factor of n! + k where k is the least positive integer such that n! + k is a square. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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.
|
|
EXAMPLE
|
a(9)=67 because 9!+729 = 363609 = 3^4*67^2 is a square with largest prime
factor of 67.
|
|
CROSSREFS
|
Cf. A068869.
Adjacent sequences: A083394 A083395 A083396 this_sequence A083398 A083399 A083400
Sequence in context: A003182 A134294 A130165 this_sequence A067362 A131200 A101595
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jason Earls (zevi_35711(AT)yahoo.com), Jun 06 2003
|
|
|
Search completed in 0.002 seconds
|
