A258613 Numbers m that are coprime to the largest square <= m, cf. A048760.

1, 2, 3, 5, 7, 10, 11, 13, 14, 17, 19, 21, 23, 26, 27, 28, 29, 31, 32, 33, 34, 37, 41, 43, 47, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 65, 67, 69, 71, 73, 75, 77, 79, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 101, 103, 107, 109, 111, 113, 117

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Joachim Lambek and Leo Moser, On integers n relatively prime to f(n), Canadian Journal of Mathematics, Vol. 7 (1955), pp. 155-158.

Formula

A074695(a(n)) = 1.

The number of terms that do not exceed x is x/zeta(2) + O(sqrt(x)*log(x)) (Lambek and Moser, 1955). - Amiram Eldar, Nov 19 2024

Example

a(8) = 13: GCD(13,A048760(13)) = GCD(13,9) = 1.
a(9) = 14: GCD(14,A048760(14)) = GCD(14,9) = 1.
GCD(15,A048760(15)) = GCD(15,9) = 3 > 1, therefore 15 is not a term.

Mathematica

Select[Range[200], CoprimeQ[#, Floor[Sqrt[#]]^2]&] (* Harvey P. Dale, Jun 25 2017 *)

Prog

(Haskell)
a258613 n = a258613_list !! (n-1)
a258613_list = filter ((== 1) . a074695) [1..]
(PARI) isok(n) = gcd(n, sqrtint(n)^2) == 1; \\ Michel Marcus, Jun 06 2015

Crossrefs

Cf. A013661, A074695, A048760, A258614 (complement).

Sequence in context: A118241 A356237 A325160 * A325460 A002269 A327445

Adjacent sequences: A258610 A258611 A258612 * A258614 A258615 A258616

Keyword

nonn

Author

Reinhard Zumkeller, Jun 05 2015

Status

approved