A258332 - OEIS

%I #22 Sep 08 2022 08:46:12

%S 211,420,722,906,2731,3687,3962,4351,4985,5505,5656,5818,6162,6443,

%T 7337,7562,7731,8293,9175,9312,9681,9861,10118,11343,11918,11931,

%U 11956,12093,12372,13646,13756,13862,14280,14618,14712,14981,15306,15716,15743,15961,16512,17162,17237

%N Numbers n such that 4n + 1, 4n + 2 and 4n + 3 are not squarefree.

%H Robert Israel, <a href="/A258332/b258332.txt">Table of n, a(n) for n = 1..10000</a>

%e 211 is in this sequence because 4 * 211 + 1 = 845 = 5 * 13^2, 4 * 211 + 2 = 846 = 2 * 3^2 * 47 and 4 * 211 + 3 = 847 = 7 * 11^2.

%p remove(t->ormap(numtheory:-issqrfree,[4*t+1,4*t+2,4*t+3]), [$1..2*10^4]); # _Robert Israel_, Apr 03 2018

%t Select[Range[1000], Union[{MoebiusMu[4# + 1], MoebiusMu[4# + 2], MoebiusMu[4# + 3]}] == {0} &] (* _Alonso del Arte_, May 26 2015 *)

%o (Magma) [n: n in [1..20000] | not IsSquarefree(4*n+1) and  not IsSquarefree(4*n+2) and not IsSquarefree(4*n+3)];

%o (PARI) isok(n) = !issquarefree(4*n+1) && !issquarefree(4*n+2) && !issquarefree(4*n+3); \\ _Michel Marcus_, Apr 04 2018

%Y Cf. A188296, A258211.

%K nonn,easy

%O 1,1

%A _Juri-Stepan Gerasimov_, May 26 2015