cp's OEIS Frontend

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

%I A055377 #31 Jul 02 2025 16:01:59
%S A055377 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 A055377 13,17,17,17,17,19,19,19,19,19,19,19,19,23,23,23,23,23,23,23,23,23,23,
%U A055377 23,23,29,29,29,29,31,31,31,31,31,31,31,31,31,31,31,31,37,37,37,37,37
%N A055377 a(n) = largest prime <= n/2.
%C A055377 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 A055377 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 A055377 a(n) is the largest prime factor whose exponent in the factorization of n! is greater than 1. - _Michel Marcus_, Nov 11 2018
%H A055377 Michael De Vlieger, <a href="/A055377/b055377.txt">Table of n, a(n) for n = 4..10000</a>
%F A055377 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 A055377 Where defined, that is for n > 2, a(A000040(n)) = A000040(A079952(n)). - _Peter Munn_, Sep 18 2017
%e A055377 n = 10, n! = 3628800, lcm[1,...,10] = 2520, A025527(10) = 1440 = 32*9*5 so a(7) = 5 (offset = 3).
%t A055377 Table[Prime@ PrimePi[n/2], {n, 4, 78}] (* _Michael De Vlieger_, Sep 21 2017 *)
%o A055377 (PARI) a(n) = precprime(n/2); \\ _Michel Marcus_, Sep 20 2017
%Y A055377 Cf. A000040, A000142, A003418, A006530, A007917, A025527, A060265, A079952, A079953.
%K A055377 nonn
%O A055377 4,1
%A A055377 _Labos Elemer_, Jun 22 2000; _David W. Wilson_, Jun 10 2005
%E A055377 More terms from _James Sellers_, Jul 04 2000
%E A055377 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 14 2007