

A118486


a(n) is the smallest prime occurring in the prime factorization of n! to an odd power.


1



2, 2, 2, 2, 5, 5, 2, 2, 7, 7, 3, 3, 2, 2, 2, 2, 5, 5, 11, 3, 2, 2, 7, 7, 2, 2, 2, 2, 5, 5, 2, 2, 3, 3, 3, 3, 2, 2, 5, 5, 2, 2, 2, 2, 3, 3, 13, 13, 2, 2, 2, 2, 17, 5, 2, 2, 3, 3, 7, 7, 2, 2, 2, 2, 3, 3, 3, 5, 2, 2, 7, 7, 2, 2, 2, 2, 11
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OFFSET

2,1


COMMENTS

If n is even then a(n) is also the smallest prime factor in the binomial coefficient C(n, n/2).


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 2..10000


EXAMPLE

a(10) = 7 since 10! = 2^8 * 3^4 * 5^2 * 7 * 11.


PROG

(PARI) a(n) = f = factor(n!); for (i=1, #f~, if (f[i, 2] % 2, return (f[i, 1]))); \\ Michel Marcus, Jun 27 2013
(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
a(n)=forprime(p=2, , if(valp(n, p)%2, return(p))) \\ Charles R Greathouse IV, Jun 27 2013


CROSSREFS

Sequence in context: A301452 A322788 A177333 * A288026 A141299 A035681
Adjacent sequences: A118483 A118484 A118485 * A118487 A118488 A118489


KEYWORD

nonn


AUTHOR

John L. Drost, Jul 21 2007


STATUS

approved



