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

%I A258614 #16 Nov 20 2024 07:40:53
%S A258614 4,6,8,9,12,15,16,18,20,22,24,25,30,35,36,38,39,40,42,44,45,46,48,49,
%T A258614 56,63,64,66,68,70,72,74,76,78,80,81,84,87,90,93,96,99,100,102,104,
%U A258614 105,106,108,110,112,114,115,116,118,120,121,132,143,144,146,147
%N A258614 Numbers m having with the largest square <= m a common divisor > 1.
%C A258614 The asymptotic density of this sequence is 1-6/Pi^2 (A229099). - _Amiram Eldar_, Nov 19 2024
%H A258614 Reinhard Zumkeller, <a href="/A258614/b258614.txt">Table of n, a(n) for n = 1..10000</a>
%F A258614 A074695(a(n)) > 1.
%e A258614 a(11) = 24: GCD(24,A048760(24)) = GCD(24,16) = 4 > 1.
%e A258614 a(12) = 25: GCD(25,A048760(25)) = GCD(25,25) = 25 > 1.
%e A258614 GCD(26,A048760(26)) = GCD(26,25) = 1, therefore 26 is not a term.
%t A258614 Select[Range[150], !CoprimeQ[#, Floor[Sqrt[#]]^2] &] (* _Amiram Eldar_, Nov 19 2024 *)
%o A258614 (Haskell)
%o A258614 a258614 n = a258614_list !! (n-1)
%o A258614 a258614_list = filter ((> 1) . a074695) [1..]
%o A258614 (PARI) isok(m) = gcd(m, sqr(sqrtint(m))) > 1; \\ _Michel Marcus_, Jan 23 2022
%Y A258614 Cf. A074695, A048760, A229099, A258613 (complement).
%K A258614 nonn
%O A258614 1,1
%A A258614 _Reinhard Zumkeller_, Jun 05 2015