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

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

1,1

Comments

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

Links

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

Formula

A074695(a(n)) > 1.

Example

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.

Mathematica

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

Prog

(Haskell)
a258614 n = a258614_list !! (n-1)
a258614_list = filter ((> 1) . a074695) [1..]
(PARI) isok(m) = gcd(m, sqr(sqrtint(m))) > 1; \\ Michel Marcus, Jan 23 2022

Crossrefs

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

Sequence in context: A161576 A327446 A100425 * A269131 A130074 A304242

Adjacent sequences: A258611 A258612 A258613 * A258615 A258616 A258617

Keyword

nonn

Author

Reinhard Zumkeller, Jun 05 2015

Status

approved