A055377 a(n) = largest prime <= n/2.

2, 2, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37

Offset

4,1

Comments

Also largest prime factor of any composite <= n. E.g., a(15) = 7 since 7 is the largest prime factor of {4,6,8,9,10,12,14,15}, the composites <= 15.

Also largest prime dividing A025527(n) = n!/lcm[1,...,n]. [Comment from Ray Chandler, Apr 26 2007: Primes > n/2 don't appear as factors of A025527(n) since they appear once in n! and again in the denominator lcm[1,...,n]. Primes <= n/2 appear more times in the numerator than the denominator so they appear in the fraction.]

a(n) is the largest prime factor whose exponent in the factorization of n! is greater than 1. - Michel Marcus, Nov 11 2018

Links

Michael De Vlieger, Table of n, a(n) for n = 4..10000

Formula

a(n) = Max(gpf((n+2) mod k): 1 < k < (n+2) and k not prime), with gpf=A006530 (greatest prime factor). - Reinhard Zumkeller, Mar 27 2004

Where defined, that is for n > 2, a(A000040(n)) = A000040(A079952(n)). - Peter Munn, Sep 18 2017

Example

n = 10, n! = 3628800, lcm[1,...,10] = 2520, A025527(10) = 1440 = 32*9*5 so a(7) = 5 (offset = 3).

Mathematica

Table[Prime@ PrimePi[n/2], {n, 4, 78}] (* Michael De Vlieger, Sep 21 2017 *)

Prog

(PARI) a(n) = precprime(n/2); \\ Michel Marcus, Sep 20 2017

Crossrefs

Cf. A000040, A000142, A003418, A006530, A007917, A025527, A060265, A079952, A079953.

Sequence in context: A160903 A124229 A355250 * A157524 A239496 A348164

Adjacent sequences: A055374 A055375 A055376 * A055378 A055379 A055380

Keyword

nonn

Author

Labos Elemer, Jun 22 2000; David W. Wilson, Jun 10 2005

Extensions

More terms from James A. Sellers, Jul 04 2000

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 14 2007

Status

approved