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Largest prime dividing phi of the n-th primorial.
3

%I #17 Sep 18 2024 02:36:26

%S 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,

%T 41,41,53,53,53,53,53,53,53,53,53,53,53,83,83,89,89,89,89,89,89,89,89,

%U 113,113,113,113,113,113,113,131,131,131,131,131,131,131,131,131,131,131

%N Largest prime dividing phi of the n-th primorial.

%H Reinhard Zumkeller, <a href="/A055769/b055769.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A006530(A000010(A002110(n))). [corrected by _Amiram Eldar_, Sep 18 2024]

%F a(n) = A006530(A005867(n)). - _Reinhard Zumkeller_, May 01 2013

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

%t Map[FactorInteger[EulerPhi@ #][[-1, 1]] &, FoldList[#1 #2 &, Prime@ Range@ 66]] (* _Michael De Vlieger_, Oct 26 2017 *)

%o (Haskell)

%o a055769 = a006530 . a005867 -- _Reinhard Zumkeller_, May 01 2013

%o (PARI) gpf(n)=my(f=factor(n)[,1]); f[#f]

%o 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

%Y Cf. A000010, A002110, A005867, A055768.

%K nonn

%O 1,2

%A _Labos Elemer_, Jul 12 2000