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

1,2

Links

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

Formula

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

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

Example

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

Mathematica

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

Prog

(Haskell)
a055769 = a006530 . a005867  -- Reinhard Zumkeller, May 01 2013
(PARI) gpf(n)=my(f=factor(n)[, 1]); f[#f]
a(n)=my(p=prime(n), q=1); while(2*q+1<p, q=max(gpf(p-1), q); p=precprime(p-1)); if(n==2, 2, q) \\ Charles R Greathouse IV, Dec 03 2014

Crossrefs

Cf. A000010, A002110, A005867, A055768.

Sequence in context: A279724 A050174 A115126 * A162217 A123575 A014200

Adjacent sequences: A055766 A055767 A055768 * A055770 A055771 A055772

Keyword

nonn

Author

Labos Elemer, Jul 12 2000

Status

approved