A279456 Numbers k such that number of distinct primes dividing k is odd and number of prime divisors (counted with multiplicity) of k is even.

4, 9, 16, 25, 49, 60, 64, 81, 84, 90, 121, 126, 132, 140, 150, 156, 169, 198, 204, 220, 228, 234, 240, 256, 260, 276, 289, 294, 306, 308, 315, 336, 340, 342, 348, 350, 360, 361, 364, 372, 380, 414, 444, 460, 476, 490, 492, 495, 504, 516, 522, 525, 528, 529, 532, 540, 550, 558, 560, 564, 572, 580, 585, 600

Offset: 1

Author

Ilya Gutkovskiy, Dec 12 2016

Keywords

• nonn
• easy

Comments

Intersection of A028260 and A030230.

Numbers k such that A000035(A001221(k)) = 1 and A000035(A001222(k)) = 0.

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

Examples

			90 is in the sequence because 90 = 2*3^2*5 therefore omega(90) = 3 {2,3,5} is odd and bigomega(90) = 4 {2,3,3,5} 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, A030230, A076479, A082522 (subsequence), A187039, A279457, A279458.

Programs

Mathematica

Select[Range[600], Mod[PrimeNu[#1], 2] == 1 && Mod[PrimeOmega[#1], 2] == 0 & ]

PARI

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