|
%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
|
