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A066856 a(n) = omega(n!+1), where omega is the number of distinct primes dividing n, A001221. 6
1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 2, 2, 2, 3, 5, 3, 6, 2, 2, 3, 3, 3, 2, 2, 2, 1, 2, 3, 5, 4, 4, 5, 2, 5, 6, 1, 2, 4, 7, 1, 3, 4, 3, 3, 3, 4, 2, 5, 5, 6, 4, 4, 2, 2, 4, 3, 4, 2, 4, 4, 3, 5, 3, 4, 5, 4, 5, 6, 5, 2, 7, 1, 4, 2, 3, 1, 6, 3, 4, 7, 3, 3, 3, 5, 5, 4, 3, 8, 3, 6, 2, 4, 3, 4, 5, 6, 6, 5, 5, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
103!+1 = 27437*31084943*C153, so a(103) is unknown until this 153-digit composite is factored. a(104) = 4 and a(105) = 6. - Rick L. Shepherd, Jun 09 2003
LINKS
William Gerst, A conjecture on the prime factorization of n!+1, arXiv:1809.07360 [math.GM], 2018.
Paul Leyland, Factors of n!+1 [Typo in URL corrected by R. J. Mathar, Nov 21 2008]
MATHEMATICA
Table[ Length[ FactorInteger[ n! + 1]], {n, 1, 15}]
PROG
(PARI) for(n=1, 64, print1(omega(n!+1), ", "))
(Magma) [#PrimeDivisors(Factorial(n) + 1): n in [1..55]]; // Vincenzo Librandi, Oct 11 2018
CROSSREFS
Cf. A054990 (bigomega(n!+1)), A002981 (n!+1 is prime), A064237 (n!+1 divisible by a square), A084846 (mu(n!+1)).
Sequence in context: A349954 A081771 A338170 * A089280 A246960 A285200
KEYWORD
hard,nonn
AUTHOR
Robert G. Wilson v, Jan 21 2002
EXTENSIONS
More terms from Rick L. Shepherd, Jun 09 2003
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)