A229109 a(n) = n plus the number of its distinct prime factors.

1, 3, 4, 5, 6, 8, 8, 9, 10, 12, 12, 14, 14, 16, 17, 17, 18, 20, 20, 22, 23, 24, 24, 26, 26, 28, 28, 30, 30, 33, 32, 33, 35, 36, 37, 38, 38, 40, 41, 42, 42, 45, 44, 46, 47, 48, 48, 50, 50, 52, 53, 54, 54, 56, 57, 58, 59, 60, 60, 63, 62, 64, 65, 65, 67, 69, 68

Offset: 1

Author

Reinhard Zumkeller, Sep 13 2013

Keywords

• nonn

Examples

			a(40) = 42, since 40 has two distinct prime divisors (2 and 5), and so 40 + 2 = 42.
a(41) = 42 also, since 41 is prime and therefore 41 + 1 = 42.
a(42) = 45, since 42 has three distinct prime divisors (2, 3, 7), and so 42 + 3 = 45.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A064800, A001221, A000961.

Programs

Haskell

a229109 n  = a001221 n + n

Mathematica

Table[n + PrimeNu[n], {n, 80}] (* Harvey P. Dale, Jun 22 2015 *)

PARI

a(n) = n + omega(n); \\ Michel Marcus, Jan 25 2022

Formula

a(n) = n + A001221(n).

a(n) = n + 1 if and only if n is prime or a power of a prime (that is, n > 1 is in A000961). - Alonso del Arte, Nov 17 2016