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A229836
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Number of primes between n! and n^n inclusive.
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1
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0, 2, 6, 45, 415, 4693, 65010, 1073640, 20669837, 454793822, 11259684418, 309761863916, 9373389023182, 309374515194621, 11059527891811334, 425655578031419604
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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There are 45 primes between 4! and 4^4 (24,256).
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MAPLE
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MATHEMATICA
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Join[{0, 2}, Table[PrimePi[n^n] - PrimePi[n!], {n, 3, 12}]] (* Wesley Ivan Hurt, Nov 17 2015 *)
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PROG
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(Python)
import math
import sympy
from sympy import sieve
x = 1
while x < 50:
....y = [i for i in sieve.primerange(math.factorial(x), x**x)]
....print(len(y))
....x += 1
(PARI) a(n) = if(n==2, 2, primepi(n^n)-primepi(n!)) \\ Altug Alkan, Nov 17 2015
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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