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A008335 Number of distinct primes dividing p+1 as p runs through the primes.

%I A008335 #17 Jul 08 2025 01:02:51
%S A008335 1,1,2,1,2,2,2,2,2,3,1,2,3,2,2,2,3,2,2,2,2,2,3,3,2,3,2,2,3,3,1,3,3,3,
%T A008335 3,2,2,2,3,3,3,3,2,2,3,2,2,2,3,3,3,3,2,3,3,3,3,2,2,3,2,3,3,3,2,3,2,2,
%U A008335 3,3,3,3,2,3,3,2,4,2,3,3,4,2,2,3,3,3,3,2,4,2,3,3,2,3,2
%N A008335 Number of distinct primes dividing p+1 as p runs through the primes.
%H A008335 T. D. Noe, <a href="/A008335/b008335.txt">Table of n, a(n) for n=1..10000</a>
%F A008335 a(n) = A001221(A008864(n)). - _Michel Marcus_, Mar 29 2016
%p A008335 for i from 1 to 500 do if isprime(i) then print(nops(factorset(i+1))); fi; od;
%t A008335 a[n_] := PrimeNu[Prime[n]+1]; Array[a, 100] (* _Amiram Eldar_, Sep 10 2024 *)
%o A008335 (PARI) a(n) = omega(prime(n)+1); \\ _Michel Marcus_, Mar 29 2016
%Y A008335 Cf. A001221, A008864, A023514.
%K A008335 nonn,easy
%O A008335 1,3
%A A008335 _N. J. A. Sloane_