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) = A001221(A000010(A002110(n))).

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