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%I #16 Sep 08 2022 08:45:15
%S 1,1,2,1,2,2,2,1,2,2,2,2,2,2,3,1,2,2,2,2,3,2,2,2,2,2,2,2,2,3,2,1,3,2,
%T 3,2,2,2,3,2,2,3,2,2,3,2,2,2,2,2,3,2,2,2,3,2,3,2,2,3,2,2,3,1,3,3,2,2,
%U 3,3,2,2,2,2,3,2,3,3,2,2,2,2,2,3,3,2,3,2,2,3,3,2,3,2,3,2,2,2,3,2,2,3,2,2,4
%N Number of distinct primes dividing 2n (i.e., omega(2n)).
%C Bisection of A001221.
%H G. C. Greubel, <a href="/A099812/b099812.txt">Table of n, a(n) for n = 1..1000</a>
%e a(6)=2 because 12 = 2*2*3 has 2 distinct prime divisors;
%e a(15)=3 because 30 = 2*3*5 has 3 distinct prime divisors.
%p 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
%t Table[PrimeNu[2*n], {n,1,50}] (* _G. C. Greubel_, May 21 2017 *)
%o (PARI) for(n=1,50, print1(omega(2*n), ", ")) \\ _G. C. Greubel_, May 21 2017
%o (Magma) [#PrimeDivisors(2*n): n in [1..100]]; // _Vincenzo Librandi_, Jul 26 2017
%Y Cf. A001221, A092523.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Nov 19 2004
%E More terms from _Emeric Deutsch_, Mar 10 2005
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