OFFSET
1,3
COMMENTS
Bisection of A001221.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
From Amiram Eldar, Sep 21 2024: (Start)
a(n) = A001221(2*n).
a(n) = omega(n) + 1 if n is odd, and a(n) = omega(n) if n is even.
Sum_{k=1..n} a(k) = n * (log(log(n)) + B + 1/2) + O(n/log(n)), where B is Mertens's constant (A077761). (End)
EXAMPLE
a(6) = 2 because 12 = 2*2*3 has 2 distinct prime divisors.
a(15) = 3 because 30 = 2*3*5 has 3 distinct prime divisors.
MAPLE
with(numtheory): omega:=proc(n) local div, A, j: div:=divisors(n): A:={}: for j from 1 to tau(n) do if isprime(div[j])=true then A:=A union {div[j]} else A:=A fi od: nops(A) end: seq(omega(2*n), n=1..130); # Emeric Deutsch, Mar 10 2005
MATHEMATICA
Table[PrimeNu[2*n], {n, 1, 50}] (* G. C. Greubel, May 21 2017 *)
PROG
(PARI) for(n=1, 50, print1(omega(2*n), ", ")) \\ G. C. Greubel, May 21 2017
(Magma) [#PrimeDivisors(2*n): n in [1..100]]; // Vincenzo Librandi, Jul 26 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 19 2004
EXTENSIONS
More terms from Emeric Deutsch, Mar 10 2005
STATUS
approved