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Numbers k such that Sum_{d|k} mu(d)*mu(k/d)^2 = +1.
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%I #23 Mar 25 2024 13:12:35

%S 1,36,100,196,225,441,484,676,1089,1156,1225,1444,1521,2116,2601,3025,

%T 3249,3364,3844,4225,4761,5476,5929,6724,7225,7396,7569,8281,8649,

%U 8836,9025,11236,12321,13225,13924,14161,14884,15129,16641,17689,17956

%N Numbers k such that Sum_{d|k} mu(d)*mu(k/d)^2 = +1.

%H Amiram Eldar, <a href="/A077448/b077448.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A030229(n)^2.

%F Sum_{n>=1} 1/a(n) = 21/(2*Pi^2). - _Amiram Eldar_, Jul 16 2020

%t Select[Range[135], MoebiusMu[#] == 1 &]^2 (* _Amiram Eldar_, Jul 16 2020 *)

%o (PARI) is(n)=if(!issquare(n,&n),return(0)); my(f=factor(n)[,2]); if(n>1, #f%2==0 && vecmax(f)==1, n==1) \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A008683, A030229, A077438, A085986 (subsequence).

%K nonn

%O 1,2

%A _Benoit Cloitre_, Nov 30 2002