A055768 Number of distinct primes dividing phi of n-th primorial number.

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, 11, 11, 11, 12, 12, 12, 12, 13, 14, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 20, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 25, 26, 26, 26, 27, 28, 28

Offset: 1

Author

Labos Elemer, Jul 12 2000

Keywords

• nonn

Examples

			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).
		

Links

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

Crossrefs

Cf. A002110, A000010, A001221, A055769.

Programs

Haskell

a055768 = a001221 . a005867  -- Reinhard Zumkeller, May 01 2013

Mathematica

Table[PrimeNu@ EulerPhi[Product[Prime@ i, {i, n}]], {n, 78}] (* or *)
With[{nn = 78}, PrimeNu@ FoldList[LCM @@ {#1, #2} &, Prime@ Range@ nn - 1]] (* Michael De Vlieger, Jul 14 2017 *)

PARI

a(n)=omega(lcm(apply(p->p-1, primes(n)))) \\ Charles R Greathouse IV, Sep 02 2015

Formula

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

a(n) < n. - Charles R Greathouse IV, Sep 02 2015