A049236 a(n) is the number of distinct prime factors of prime(n) + 2.

1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 3, 2, 3, 2, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 1, 2

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Examples

			prime(27) = 103, prime(27) + 2 = 105 = 3*5*7 has 3 prime factors, so a(27) = 3.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001221, A001359, A052147, A064909, A064910, A064911.

Programs

Mathematica

Table[Length[FactorInteger[Prime[n] + 2]], {n, 1, 50}] (* G. C. Greubel, May 12 2017 *)

PARI

a(n) = omega(prime(n) + 2); \\ Amiram Eldar, Sep 16 2024

Formula

a(n) = A001221(A052147(n)). - Amiram Eldar, Sep 16 2024