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A332444 Numbers k that are squares or twice-squares, but for which A087808(sigma(k)) is even.

%I A332444 #11 Feb 15 2020 08:05:08
%S A332444 2,8,32,36,72,98,128,144,162,196,225,242,288,289,324,484,512,576,882,
%T A332444 968,1058,1152,1444,1458,1521,1681,1764,1922,1936,2048,2178,2304,2500,
%U A332444 2809,2888,2916,3025,3528,3698,3872,4418,4608,4802,5000,5329,5776,5832,6498,7056,7396,7569,7688,7744,7921,7938,8192,8281
%N A332444 Numbers k that are squares or twice-squares, but for which A087808(sigma(k)) is even.
%C A332444 Numbers k for which A000203(k) is odd and A332224(k) is even.
%H A332444 Antti Karttunen, <a href="/A332444/b332444.txt">Table of n, a(n) for n = 1..19515</a>
%H A332444 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A332444 (PARI)
%o A332444 A087808(n) = if(n<1, 0, if(n%2==0, 2*A087808(n/2), A087808((n-1)/2)+1));
%o A332444 isA332444(n) = (((!(n%2)&&issquare(n/2))||issquare(n)) && !(A087808(sigma(n))%2));
%o A332444 A332444list(u) = { my(v1=vector(2*u,n,2*(n^2)), v2=vector(sqrtint(v1[#v1]),n,n^2)); select(isA332444,Vec(setunion(v1,v2))); };
%o A332444 v332444 = A332444list(12000);
%o A332444 A332444(n) = v332444[n];
%Y A332444 Setwise difference of A028982 \ A332443.
%Y A332444 Cf. A000203, A087808, A332224, A332225.
%K A332444 nonn
%O A332444 1,1
%A A332444 _Antti Karttunen_, Feb 13 2020