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%I #7 Feb 23 2024 11:03:35
%S 2,6,8,10,14,18,22,26,30,32,34,38,40,42,46,50,54,56,58,62,66,70,74,78,
%T 82,86,88,90,94,96,98,102,104,106,110,114,118,122,126,128,130,134,136,
%U 138,142,146,150,152,154,158,162,166,170,174,178,182,184,186,190,194,198,200
%N Even numbers k such that gcd(k, A007814(k)) = 1.
%C The asymptotic density of this sequence is Sum_{k>=0} (phi(2*k+1)/((2*k+1)*2^(2*k+2))) = 0.30845704942203403516..., where phi is Euler's totient function (A000010).
%H Amiram Eldar, <a href="/A370597/b370597.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[2 * Range[200], CoprimeQ[#, IntegerExponent[#, 2]] &]
%o (PARI) is(n) = !(n%2) && gcd(n, valuation(n, 2)) == 1;
%Y Cf. A000010, A007814, A336066.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Feb 23 2024
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