A370597 Even numbers k such that gcd(k, A007814(k)) = 1.

2, 6, 8, 10, 14, 18, 22, 26, 30, 32, 34, 38, 40, 42, 46, 50, 54, 56, 58, 62, 66, 70, 74, 78, 82, 86, 88, 90, 94, 96, 98, 102, 104, 106, 110, 114, 118, 122, 126, 128, 130, 134, 136, 138, 142, 146, 150, 152, 154, 158, 162, 166, 170, 174, 178, 182, 184, 186, 190, 194, 198, 200

Offset: 1

Author

Amiram Eldar, Feb 23 2024

Keywords

• nonn
• easy

Comments

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).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A007814, A336066.

Programs

Mathematica

Select[2 * Range[200], CoprimeQ[#, IntegerExponent[#, 2]] &]

PARI

is(n) = !(n%2) && gcd(n, valuation(n, 2)) == 1;