A117204 - OEIS

A117204

Squarefree positive integers k such that 2*k+1 is also squarefree.

1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 17, 19, 21, 23, 26, 29, 30, 33, 34, 35, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 59, 61, 65, 66, 69, 70, 71, 74, 77, 78, 79, 82, 83, 86, 89, 91, 93, 95, 97, 101, 102, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119

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OFFSET

1,2

COMMENTS

The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (Erdős and Ivić, 1987). - Amiram Eldar, Mar 02 2021

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

Paul Erdős and Aleksandar Ivić, The distribution of values of a certain class of arithmetic functions at consecutive integers, Colloq. Math. Soc. János Bolyai, Vol. 51 (1987), pp. 45-91.

FORMULA

a(n) = (A117203(n) - 1)/2.

EXAMPLE

10 and 2*10 +1 = 21 are both squarefree, so 10 is in the sequence.