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

1,4

Links

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

Formula

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

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

Example

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).

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 *)

Prog

(Haskell)
a055768 = a001221 . a005867  -- Reinhard Zumkeller, May 01 2013
(PARI) a(n)=omega(lcm(apply(p->p-1, primes(n)))) \\ Charles R Greathouse IV, Sep 02 2015

Crossrefs

Cf. A002110, A000010, A001221, A055769.

Sequence in context: A078428 A337634 A316355 * A349909 A064952 A255070

Adjacent sequences: A055765 A055766 A055767 * A055769 A055770 A055771

Keyword

nonn

Author

Labos Elemer, Jul 12 2000

Status

approved