A279458 Numbers k such that number of distinct primes dividing k is even and number of prime divisors (counted with multiplicity) of k is even.

1, 6, 10, 14, 15, 21, 22, 24, 26, 33, 34, 35, 36, 38, 39, 40, 46, 51, 54, 55, 56, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 88, 91, 93, 94, 95, 96, 100, 104, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 135, 136, 141, 142, 143, 144, 145, 146, 152, 155, 158, 159, 160, 161, 166, 177, 178, 183, 184, 185, 187, 189

Offset: 1

Author

Ilya Gutkovskiy, Dec 12 2016

Keywords

• nonn
• easy

Comments

Intersection of A028260 and A030231.

Numbers k such that A000035(A001221(k)) = 0 and A000035(A001222(k)) = 0.

Numbers k such that A076479(k) = 1 and A008836(k) = 1.

Examples

			24 is in the sequence because 24 = 2^3*3 therefore omega(24) = 2 {2,3} is even and bigomega(24) = 4 {2,2,2,3} is even.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Distinct Prime Factors.
• Eric Weisstein's World of Mathematics, Prime Factor.

Crossrefs

Cf. A000035, A001221, A001222, A008836, A028260, A030231, A076479, A279456, A279457.

Programs

Mathematica

Select[Range[220], Mod[PrimeNu[#1], 2] == Mod[PrimeOmega[#1], 2] == 0 & ]

PARI

is(k) = {my(f = factor(k)); !(omega(f) % 2) && !(bigomega(f) % 2);} \\ Amiram Eldar, Sep 17 2024