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Number of distinct primes dividing phi of n-th primorial number.
4

%I #13 Jul 14 2017 22:22:30

%S 0,1,1,2,3,3,3,3,4,5,5,5,5,5,6,7,8,8,8,8,8,8,9,9,9,9,10,11,11,11,11,

%T 11,11,11,12,12,12,12,13,14,15,15,16,16,16,16,16,16,17,17,17,17,17,17,

%U 17,18,19,19,19,19,20,21,21,22,22,23,23,23,24,24,24,25,26,26,26,27,28,28

%N Number of distinct primes dividing phi of n-th primorial number.

%H Reinhard Zumkeller, <a href="/A055768/b055768.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001221(A000010(A002110(n))) = A001221(A005867(n)).

%F a(n) < n. - _Charles R Greathouse IV_, Sep 02 2015

%e For primorials with 10, 100, or 1000 prime factors, their totients have only 5, 32 or 241 prime divisors, corresponding to a(10), a(100), and a(1000).

%t Table[PrimeNu@ EulerPhi[Product[Prime@ i, {i, n}]], {n, 78}] (* or *)

%t With[{nn = 78}, PrimeNu@ FoldList[LCM @@ {#1, #2} &, Prime@ Range@ nn - 1]] (* _Michael De Vlieger_, Jul 14 2017 *)

%o (Haskell)

%o a055768 = a001221 . a005867 -- _Reinhard Zumkeller_, May 01 2013

%o (PARI) a(n)=omega(lcm(apply(p->p-1, primes(n)))) \\ _Charles R Greathouse IV_, Sep 02 2015

%Y Cf. A002110, A000010, A001221, A055769.

%K nonn

%O 1,4

%A _Labos Elemer_, Jul 12 2000