A258613 -id:A258613 - 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

A258614 Numbers m having with the largest square <= m a common divisor > 1.

Original entry on oeis.org

4, 6, 8, 9, 12, 15, 16, 18, 20, 22, 24, 25, 30, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 56, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 84, 87, 90, 93, 96, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 118, 120, 121, 132, 143, 144, 146, 147

Offset: 1

Reinhard Zumkeller, Jun 05 2015

nonn

The asymptotic density of this sequence is 1-6/Pi^2 (A229099). - Amiram Eldar, Nov 19 2024

			a(11) = 24: GCD(24,A048760(24)) = GCD(24,16) = 4 > 1.
a(12) = 25: GCD(25,A048760(25)) = GCD(25,25) = 25 > 1.
GCD(26,A048760(26)) = GCD(26,25) = 1, therefore 26 is not a term.

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

Cf. A074695, A048760, A229099, A258613 (complement).

a258614 n = a258614_list !! (n-1)
a258614_list = filter ((> 1) . a074695) [1..]

Select[Range[150], !CoprimeQ[#, Floor[Sqrt[#]]^2] &] (* Amiram Eldar, Nov 19 2024 *)

isok(m) = gcd(m, sqr(sqrtint(m))) > 1; \\ Michel Marcus, Jan 23 2022

A074695(a(n)) > 1.

cp's OEIS Frontend

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

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