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A008328 Number of divisors of prime(n)-1. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
Karl Prachar, Über die Anzahl der Teiler einer natürlichen Zahl, welche die Form p-1 haben, Monatshefte für Mathematik, Vol. 59 (1955), pp. 91-97.
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial.
FORMULA
a(n) = A000005(A006093(n)) = A066800(prime(n)). - R. J. Mathar, Oct 01 2017
From Amiram Eldar, Apr 16 2024: (Start)
Formulas from Prachar (1955):
Sum_{prime(n) < x} a(n) = x * log(log(x)) + B*x + O(x/log(x)), where B is a constant.
There is a constant c > 0 such that for infinitely many values of n we have a(n) > exp(c * log(prime(n))/log(log(prime(n))))). (End)
MAPLE
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
MATHEMATICA
DivisorSigma[0, #-1]&/@Prime[Range[90]] (* Harvey P. Dale, Dec 08 2011 *)
PROG
(PARI) a(n) = numdiv(prime(n)-1); \\ Michel Marcus, Feb 25 2021
CROSSREFS
Sequence in context: A008329 A064558 A178031 * A298933 A365851 A091860
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 12 17:45 EDT 2024. Contains 374251 sequences. (Running on oeis4.)