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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 19 18:25 EST 2020. Contains 331051 sequences. (Running on oeis4.)