A118486 a(n) is the smallest prime occurring in the prime factorization of n! to an odd power.

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

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: A337082 A333505 A177333 * A288026 A141299 A035681

Adjacent sequences: A118483 A118484 A118485 * A118487 A118488 A118489

Keyword

nonn

Author

John L. Drost, Jul 21 2007

Status

approved