OFFSET
1,2
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).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Willy Feller and Erhard Tornier, Mengentheoretische Untersuchung von Eigenschaften der Zahlenreihe, Mathematische Annalen, Vol. 107 (1933), pp. 188-232.
I. J. Schoenberg, On asymptotic distributions of arithmetical functions, Transactions of the American Mathematical Society, Vol. 39, No. 2 (1936), pp. 315-330. See p. 326.
Eric Weisstein's World of Mathematics, Feller-Tornier Constant.
Wikipedia, Feller-Tornier constant.
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] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 23 2020
STATUS
approved