A055769 Largest prime dividing phi of the n-th primorial.

1, 2, 2, 3, 5, 5, 5, 5, 11, 11, 11, 11, 11, 11, 23, 23, 29, 29, 29, 29, 29, 29, 41, 41, 41, 41, 41, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 83, 83, 89, 89, 89, 89, 89, 89, 89, 89, 113, 113, 113, 113, 113, 113, 113, 131, 131, 131, 131, 131, 131, 131, 131, 131, 131, 131

Offset: 1

Author

Labos Elemer, Jul 12 2000

Keywords

• nonn

Examples

			While the largest prime factors of 10th, 100th or 1000th primorials are 29, 541, 7919, those of their totients are 11, 251, 3911, respectively.
		

Links

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

Crossrefs

Cf. A000010, A002110, A005867, A055768.

Programs

Haskell

a055769 = a006530 . a005867  -- Reinhard Zumkeller, May 01 2013

Mathematica

Map[FactorInteger[EulerPhi@ #][[-1, 1]] &, FoldList[#1 #2 &, Prime@ Range@ 66]] (* Michael De Vlieger, Oct 26 2017 *)

PARI

gpf(n)=my(f=factor(n)[,1]); f[#f]
a(n)=my(p=prime(n),q=1); while(2*q+1Charles R Greathouse IV, Dec 03 2014

Formula

a(n) = A006530(A000010(A002110(n))). [corrected by Amiram Eldar, Sep 18 2024]

a(n) = A006530(A005867(n)). - Reinhard Zumkeller, May 01 2013