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A008328
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Number of divisors of prime(n)-1.
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13
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1, 2, 3, 4, 4, 6, 5, 6, 4, 6, 8, 9, 8, 8, 4, 6, 4, 12, 8, 8, 12, 8, 4, 8, 12, 9, 8, 4, 12, 10, 12, 8, 8, 8, 6, 12, 12, 10, 4, 6, 4, 18, 8, 14, 9, 12, 16, 8, 4, 12, 8, 8, 20, 8, 9, 4, 6, 16, 12, 16, 8, 6, 12, 8, 16, 6, 16, 20, 4, 12, 12, 4, 8, 12, 16, 4, 6, 18, 15, 16, 8, 24, 8
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OFFSET
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1,2
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COMMENTS
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Also the number of irreducible factors of Phi(p,x)-1, for cyclotomic polynomial Phi(p,x) and prime p. The formula is Phi(p,x)-1 = x*Product_{n>1, n|p-1} Phi(n,x). - T. D. Noe, Oct 17 2003
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
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FORMULA
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a(n) = A000005(A006093(n)) = A066800(prime(n)). - R. J. Mathar, Oct 01 2017
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MAPLE
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for i from 1 to 500 do if isprime(i) then print(tau(i-1)); fi; od;
A008328 := proc(n)
numtheory[tau](ithprime(n)-1) ;
end proc: # R. J. Mathar, Oct 30 2015
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MATHEMATICA
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DivisorSigma[0, #-1]&/@Prime[Range[90]] (* Harvey P. Dale, Dec 08 2011 *)
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PROG
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(PARI) a(n) = numdiv(prime(n)-1); \\ Michel Marcus, Feb 25 2021
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CROSSREFS
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Cf. A000005, A006093, A066800.
Sequence in context: A008329 A064558 A178031 * A298933 A091860 A333995
Adjacent sequences: A008325 A008326 A008327 * A008329 A008330 A008331
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KEYWORD
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nonn,changed
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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