A333634 - OEIS (original) (raw)

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 100, 101, 102

COMMENTS

Numbers that have an even number of distinct prime factors raised to a power larger than 1.

The asymptotic density of this sequence is 0.661317... (A065493, Feller and Tornier, 1933).

FORMULA

Numbers k with A056170(k) == 0 (mod 2).

EXAMPLE

1 is a term since it has 0 prime divisors, and 0 is even.

180 is a term since 180 = 2^2 * 3^2 * 5 has 2 prime divisors, 2 and 3, with exponents larger than 1 in its prime factorization, and 2 is even.

MATHEMATICA

Select[Range[100], EvenQ @ Count[FactorInteger[#][[;; , 2]], u_ /; u > 1] &]