

A229109


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


5



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
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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


CROSSREFS

Cf. A064800.
Sequence in context: A084919 A153100 A143152 * A096127 A327953 A112768
Adjacent sequences: A229106 A229107 A229108 * A229110 A229111 A229112


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Sep 13 2013


STATUS

approved



