A117366 a(n) = smallest prime greater than the largest prime dividing n.

2, 3, 5, 3, 7, 5, 11, 3, 5, 7, 13, 5, 17, 11, 7, 3, 19, 5, 23, 7, 11, 13, 29, 5, 7, 17, 5, 11, 31, 7, 37, 3, 13, 19, 11, 5, 41, 23, 17, 7, 43, 11, 47, 13, 7, 29, 53, 5, 11, 7, 19, 17, 59, 5, 13, 11, 23, 31, 61, 7, 67, 37, 11, 3, 17, 13, 71, 19, 29, 11, 73, 5, 79, 41, 7, 23, 13, 17, 83, 7

Offset: 1

Author

Leroy Quet, Mar 10 2006

Keywords

• nonn

Examples

			5 is the largest prime dividing 10. So a(10) is the smallest prime > 5, which is 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A117364, A117365, A117367.

Cf. A000040, A006530, A151800, A159081.

Programs

Haskell

a117366 = a151800 . a006530  -- Reinhard Zumkeller, Apr 06 2015

Mathematica

Table[Prime[PrimePi[FactorInteger[n][[Length[FactorInteger[n]]]][[1]]]+1], {n, 80}] (* Stefan Steinerberger, Apr 09 2006 *)

PARI

A117366(n) = if(1==n, 2, nextprime(1+vecmax(factor(n)[, 1]))); \\ Antti Karttunen, Jan 15 2020

Formula

a(n) = A151800(A006530(n)). - Reinhard Zumkeller, Apr 06 2015

a(n) = A000040(A159081(n)). - Antti Karttunen, Jan 15 2020

Extensions

More terms from Stefan Steinerberger, Apr 09 2006