A258614 -id:A258614 - cp's OEIS frontend

A074695 Greatest common divisor of n and floor(n^(1/2))^2.

1, 1, 1, 4, 1, 2, 1, 4, 9, 1, 1, 3, 1, 1, 3, 16, 1, 2, 1, 4, 1, 2, 1, 8, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 36, 1, 2, 3, 4, 1, 6, 1, 4, 9, 2, 1, 12, 49, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 64, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 81, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 100

Offset: 1

Reinhard Zumkeller, Sep 03 2002

nonn

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

Cf. A000196, A000290, A048760.

Cf. A258613, A258614.

a074695 n = gcd n $ a048760 n  -- Reinhard Zumkeller, Jun 05 2015

Table[GCD[n,Floor[Sqrt[n]]^2],{n,100}] (* Harvey P. Dale, Aug 12 2018 *)

a(n) = gcd(n, sqrtint(n)^2); \\ Amiram Eldar, Nov 19 2024

a(n) = GCD(n, A048760(n)).
a(n) = n iff n is a square.
a(A258613(n)) = 1; a(A258614(n)) > 1. - Reinhard Zumkeller, Jun 05 2015

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

Original entry on oeis.org

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

Reinhard Zumkeller, Jun 05 2015

nonn

			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.

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.

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

a258613 n = a258613_list !! (n-1)
a258613_list = filter ((== 1) . a074695) [1..]

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

isok(n) = gcd(n, sqrtint(n)^2) == 1; \\ Michel Marcus, Jun 06 2015

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

cp's OEIS Frontend

A074695 Greatest common divisor of n and floor(n^(1/2))^2.

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