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Numbers m such that 5*m is squarefree.
6

%I #44 Sep 26 2023 01:57:52

%S 1,2,3,6,7,11,13,14,17,19,21,22,23,26,29,31,33,34,37,38,39,41,42,43,

%T 46,47,51,53,57,58,59,61,62,66,67,69,71,73,74,77,78,79,82,83,86,87,89,

%U 91,93,94,97,101,102,103,106,107,109,111,113,114,118,119,122,123,127,129,131,133,134

%N Numbers m such that 5*m is squarefree.

%C Squarefree numbers coprime to 5.

%H Amiram Eldar, <a href="/A274546/b274546.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ Pi^2*n/5. - _Charles R Greathouse IV_, Sep 06 2016 [corrected by _Amiram Eldar_, Sep 26 2023]

%F Sum_{n>=1} 1/a(n)^s = (5^s)*zeta(s)/((1+5^s)*zeta(2*s)), s>1. - _Amiram Eldar_, Sep 26 2023

%e 6 is in this sequence because 5*6 = 30 = 2*3*5 is squarefree.

%t Select[Range[135], !Divisible[#, 5] && SquareFreeQ[#] &] (* _Amiram Eldar_, Sep 26 2023 *)

%o (Magma) [n: n in [1..135] | IsSquarefree(5*n)];

%o (PARI) lista(nn) = for(n=1, nn, if(issquarefree(5*n), print1(n, ", "))); \\ _Altug Alkan_, Sep 05 2016

%o (PARI) is(n)=n%5 && issquarefree(n) \\ _Charles R Greathouse IV_, Sep 06 2016

%Y Numbers m such that m*A005117(k) is squarefree: A005117 (k = 1), A056911 (k = 2), A261034 (k = 3), this sequence (k = 5), A276378 (k = 6).

%Y Cf. A008587.

%K nonn,easy

%O 1,2

%A _Juri-Stepan Gerasimov_, Sep 05 2016