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A279456 Numbers n such that number of distinct primes dividing n is odd and number of prime divisors (counted with multiplicity) of n is even. 4

%I #13 May 08 2017 07:22:50

%S 4,9,16,25,49,60,64,81,84,90,121,126,132,140,150,156,169,198,204,220,

%T 228,234,240,256,260,276,289,294,306,308,315,336,340,342,348,350,360,

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

%C Intersection of A028260 and A030230.

%C Numbers n such that A000035(A001221(n)) = 1 and A000035(A001222(n)) = 0.

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

%H G. C. Greubel, <a href="/A279456/b279456.txt">Table of n, a(n) for n = 1..1000</a>

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

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

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

%Y Cf. A000035, A001221, A001222, A008836, A028260, A030230, A076479, A082522 (subsequence), A187039, A279457, A279458.

%K nonn,easy

%O 1,1

%A _Ilya Gutkovskiy_, Dec 12 2016

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)