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%I #7 Mar 08 2024 08:04:56
%S 4,8,9,16,18,25,32,36,49,50,64,72,81,98,100,121,125,128,144,162,169,
%T 196,200,225,242,245,250,256,288,289,324,338,361,392,400,441,450,484,
%U 490,500,512,529,576,578,605,625,648,676,722,729,784,800,841,845,882,900,961,968,980,1000
%N Numbers that are the sum of 2 squares and divisible by the square of their largest prime factor.
%C The asymptotic density of this sequence within A001481 is zero. More precisely, the number of terms that do not exceed x is ~ o(x/sqrt(log(x))) (Jakimczuk, 2024, Theorem 4.10, p. 55).
%H Amiram Eldar, <a href="/A371013/b371013.txt">Table of n, a(n) for n = 1..10000</a>
%H Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.27745.48487">Generalizations of Mertens's Formula and k-Free and s-Full Numbers with Prime Divisors in Arithmetic Progression</a>, ResearchGate, 2024.
%t Select[Range[1500], SquaresR[2, #] > 0 && FactorInteger[#][[-1 , 2]] > 1 &]
%o (PARI) is(n) = {my(f=factor(n)); if(n == 1 || f[#f~, 2] == 1, return(0)); for(i=1, #f~, if(f[i, 2]%2 && f[i, 1]%4 == 3, return(0))); 1;}
%Y Intersection of A001481 and A070003.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Mar 08 2024
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