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

1,2

Links

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

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

Example

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.

Mathematica

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

Prog

(Haskell)
a229109 n  = a001221 n + n
(PARI) a(n) = n + omega(n); \\ Michel Marcus, Jan 25 2022

Crossrefs

Cf. A064800, A001221, A000961.

Sequence in context: A084919 A153100 A143152 * A096127 A327953 A352025

Adjacent sequences: A229106 A229107 A229108 * A229110 A229111 A229112

Keyword

nonn

Author

Reinhard Zumkeller, Sep 13 2013

Status

approved