[seqfan] A061057 and A158207 are the same

Prof. Dr. Alois Heinz heinz at hs-heilbronn.de
Tue Jul 7 02:17:57 CEST 2009

Both sequences are essentially the same:
(as conjectured by Richard Mathar)

(here the displayed number a(6)=2 is not correct, but the given
Maple program computes correct value a(6)=6=30-24.)

n! will never be the square of an integer, because of primes in the last
half of the factors. Therefore the divisors of n! come in pairs (x,y) with
x*y=n! and x<y. Both sequences give the difference y-x of the pair nearest
to the square root of n!.


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