A158584 Erroneous version of A079866.

2, 3, 1, 5, 2, 7, 1, 3, 3, 11, 2, 13, 3, 3, 1, 17, 2, 19, 2, 4, 4, 23, 2, 4, 5, 3, 3, 29, 3, 31, 1, 5, 5, 5, 2, 37, 6, 6, 2, 41, 3, 43, 3, 3, 6, 47, 2, 7, 3, 7, 3, 53, 2, 7, 2, 7, 7, 59, 2, 61, 7, 3, 1, 8, 4, 67, 4, 8, 4, 71, 2, 73, 8, 4, 4, 8, 4, 79, 2, 3, 9, 83, 3, 9, 9, 9, 3, 89, 3, 9, 4, 9, 9, 9, 2, 97

Offset: 2

Author

Cino Hilliard, Mar 21 2009

Keywords

• dead

Comments

We do not begin with the unit 1 because it has no prime factors. Conjecture: The sequence contains the set of prime numbers more than once.

Examples

			12=2*2*3 has 3 factors; 12^(1/3) = 2.289428... so 2 is in the 11th position in the sequence.
		

Programs

PARI

g(n) = for(x=2,n,print1(floor(x^(1/bigomega(x)))","))

Formula

The geometric mean is the n-th root of the product of n numbers.

Gm = (a(1)*a(2)*...*a(n))^(1/n).