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A333634
Numbers with an even number of non-unitary prime divisors.
9
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
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
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.
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
Cf. A056170, A065493, A190641, A327877 (complement).
Sequence in context: A325511 A240370 A193304 * A348499 A336223 A348961
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 23 2020
STATUS
approved