

A055768


Number of distinct primes dividing phi of nth primorial number.


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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>p1, primes(n)))) \\ Charles R Greathouse IV, Sep 02 2015


CROSSREFS

Cf. A002110, A000010, A001221, A055769.
Sequence in context: A078428 A337634 A316355 * A064952 A255070 A176001
Adjacent sequences: A055765 A055766 A055767 * A055769 A055770 A055771


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 12 2000


STATUS

approved



