cp's OEIS Frontend

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.

%I A279456 #19 Feb 16 2025 08:33:37
%S A279456 4,9,16,25,49,60,64,81,84,90,121,126,132,140,150,156,169,198,204,220,
%T A279456 228,234,240,256,260,276,289,294,306,308,315,336,340,342,348,350,360,
%U A279456 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
%N 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.
%C A279456 Intersection of A028260 and A030230.
%C A279456 Numbers k such that A000035(A001221(k)) = 1 and A000035(A001222(k)) = 0.
%C A279456 Numbers k such that A076479(k) = -1 and A008836(k) = 1.
%H A279456 G. C. Greubel, <a href="/A279456/b279456.txt">Table of n, a(n) for n = 1..1000</a>
%H A279456 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.
%H A279456 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>.
%e A279456 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.
%t A279456 Select[Range[600], Mod[PrimeNu[#1], 2] == 1 && Mod[PrimeOmega[#1], 2] == 0 & ]
%o A279456 (PARI) is(k) = {my(f = factor(k)); omega(f) % 2 && !(bigomega(f) % 2);} \\ _Amiram Eldar_, Sep 17 2024
%Y A279456 Cf. A000035, A001221, A001222, A008836, A028260, A030230, A076479, A082522 (subsequence), A187039, A279457, A279458.
%K A279456 nonn,easy
%O A279456 1,1
%A A279456 _Ilya Gutkovskiy_, Dec 12 2016