login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055377 a(n) = largest prime <= n/2. 3

%I

%S 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,

%T 13,17,17,17,17,19,19,19,19,19,19,19,19,23,23,23,23,23,23,23,23,23,23,

%U 23,23,29,29,29,29,31,31,31,31,31,31,31,31,31,31,31,31,37,37,37,37,37

%N a(n) = largest prime <= n/2.

%C 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.

%C 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.]

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

%H Michael De Vlieger, <a href="/A055377/b055377.txt">Table of n, a(n) for n = 4..10000</a>

%F 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

%F Where defined, that is for n > 2, a(A000040(n)) = A000040(A079952(n)). - _Peter Munn_, Sep 18 2017

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

%t Table[Prime@ PrimePi[n/2], {n, 4, 78}] (* _Michael De Vlieger_, Sep 21 2017 *)

%o (PARI) a(n) = precprime(n/2); \\ _Michel Marcus_, Sep 20 2017

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

%K nonn

%O 4,1

%A _Labos Elemer_, Jun 22 2000; _David W. Wilson_, Jun 10 2005

%E More terms from _James A. Sellers_, Jul 04 2000

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 14 2007

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)