A279458 - OEIS

%I #21 Sep 18 2024 08:29:22

%S 1,6,10,14,15,21,22,24,26,33,34,35,36,38,39,40,46,51,54,55,56,57,58,

%T 62,65,69,74,77,82,85,86,87,88,91,93,94,95,96,100,104,106,111,115,118,

%U 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

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

%C Intersection of A028260 and A030231.

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

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

%H G. C. Greubel, <a href="/A279458/b279458.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>.

%e 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.

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

%o (PARI) is(k) = {my(f = factor(k)); !(omega(f) % 2) && !(bigomega(f) % 2);} \\ _Amiram Eldar_, Sep 17 2024

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

%K nonn,easy,changed

%O 1,2

%A _Ilya Gutkovskiy_, Dec 12 2016