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A099812 Number of distinct primes dividing 2n (i.e., omega(2n)). 2
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Bisection of A001221.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Cf. A001221, A092523.

Sequence in context: A201219 A254315 A080942 * A246600 A068068 A193523

Adjacent sequences:  A099809 A099810 A099811 * A099813 A099814 A099815

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 19 2004

EXTENSIONS

More terms from Emeric Deutsch, Mar 10 2005

STATUS

approved

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Last modified February 19 10:54 EST 2019. Contains 320310 sequences. (Running on oeis4.)