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A083397 Largest prime factor of n! + k where k is the least positive integer such that n! + k is a square. 0

%I

%S 0,2,3,5,11,3,71,67,67,127,13,509,137,37,71471,71471,409993,941351,

%T 24419,287093,7147792819,110647261,80392811773,4716679469,4716679469,

%U 323905128133,8392290961,551615338229,34178276390953,73669621631

%N Largest prime factor of n! + k where k is the least positive integer such that n! + k is a square.

%C 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.

%e a(9)=67 because 9!+729 = 363609 = 3^4*67^2 is a square with largest prime

%e factor of 67.

%t Join[{0},Table[FactorInteger[(Floor[Sqrt[n!]]+1)^2][[-1,1]],{n,2,30}]] (* _Harvey P. Dale_, Jan 04 2012 *)

%Y Cf. A068869.

%K easy,nonn

%O 1,2

%A _Jason Earls_, Jun 06 2003

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)