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A003604
Number of primes <= n!.
(Formerly M2815)
17
0, 0, 1, 3, 9, 30, 128, 675, 4231, 30969, 258689, 2428956, 25306287, 289620751, 3610490805, 48686912930, 706003798139, 10953617995740, 181035032207760, 3175094503778521, 58893601709552538, 1151825702178908788, 23688535118132456668, 511050155316058710033
OFFSET
0,4
COMMENTS
Number of distinct prime divisors of (n!)!, (A000197). - Jason Earls, Jul 04 2001
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
MATHEMATICA
Table[PrimePi[n!], {n, 0, 16}]
PROG
(PARI) for(n=0, 10, print(omega(n!!)))
(PARI) a(n)=primepi(n!) \\ Charles R Greathouse IV, Jan 21 2016
(Sage) [prime_pi(factorial(n)) for n in range(0, 14)] # Zerinvary Lajos, Jun 06 2009
CROSSREFS
Sequence in context: A297202 A377394 A370439 * A357615 A292300 A058148
KEYWORD
hard,nonn
EXTENSIONS
a(15) from Jud McCranie
a(16)-a(17) from Paul Zimmermann
a(18) from Donovan Johnson, Dec 18 2009
a(19) from Donovan Johnson, Feb 18 2010
a(20) from Henri Lifchitz, Nov 11 2012
a(21)-a(23) from Henri Lifchitz, Aug 26 2014
STATUS
approved