A008334 Number of distinct primes dividing p-1, where p = n-th prime.

0, 1, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 2, 3, 3, 2, 2, 3, 4, 3, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 4, 3, 2, 3, 2, 2, 3, 3, 3, 2, 2, 3, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 4, 2, 2, 2, 3, 3

Offset

1,4

Comments

This is omega(p-1), i.e. A001221(A006093(n)). For Omega(p-1) = A001222(A006093(n)), see A023508. - Lekraj Beedassy, Oct 08 2004

Primes counted without multiplicity. - Harvey P. Dale, May 05 2018

References

N. P. Ryzhova, Asymptotic formulae in a binary problem of shifted prime numbers (in Russian), Additive problems of number theory, Interuniv. Collect. Sci. Works, Kujbyshev 1985 (1985), pp. 25-31.

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Formula

Sum_{k=1..n} a(k) ~ n*log(log(n))/log(n) + O(n/log(n)) (Ryzhova, 1985). - Amiram Eldar, Mar 05 2021

Maple

for i from 1 to 500 do if isprime(i) then print(nops(factorset(i-1))); fi; od;

Mathematica

PrimeNu[#]&/@(Prime[Range[100]]-1) (* Harvey P. Dale, May 05 2018 *)

Crossrefs

Cf. A001221, A001222, A006093, A023508.

Sequence in context: A097195 A274138 A179301 * A116858 A182134 A189684

Adjacent sequences: A008331 A008332 A008333 * A008335 A008336 A008337

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Definition clarified by Harvey P. Dale, May 05 2018

Status

approved