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a(n) = n plus the number of its distinct prime factors.
6

%I #22 Jan 25 2022 12:25:38

%S 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,

%T 28,28,30,30,33,32,33,35,36,37,38,38,40,41,42,42,45,44,46,47,48,48,50,

%U 50,52,53,54,54,56,57,58,59,60,60,63,62,64,65,65,67,69,68

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

%H Reinhard Zumkeller, <a href="/A229109/b229109.txt">Table of n, a(n) for n = 1..10000</a>

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

%F 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

%e a(40) = 42, since 40 has two distinct prime divisors (2 and 5), and so 40 + 2 = 42.

%e a(41) = 42 also, since 41 is prime and therefore 41 + 1 = 42.

%e a(42) = 45, since 42 has three distinct prime divisors (2, 3, 7), and so 42 + 3 = 45.

%t Table[n + PrimeNu[n], {n, 80}] (* _Harvey P. Dale_, Jun 22 2015 *)

%o (Haskell)

%o a229109 n = a001221 n + n

%o (PARI) a(n) = n + omega(n); \\ _Michel Marcus_, Jan 25 2022

%Y Cf. A064800, A001221, A000961.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Sep 13 2013