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Squared radii of circles centered at a grid point in a square lattice hitting exactly 4 points. Indices k such that A004018(k)=4.
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%I #13 Jun 14 2017 00:19:25

%S 1,2,4,8,9,16,18,32,36,49,64,72,81,98,121,128,144,162,196,242,256,288,

%T 324,361,392,441,484,512,529,576,648,722,729,784,882,961,968,1024,

%U 1058,1089,1152,1296,1444,1458,1568,1764,1849,1922,1936,2048,2116,2178,2209

%N Squared radii of circles centered at a grid point in a square lattice hitting exactly 4 points. Indices k such that A004018(k)=4.

%C From _Jean-Christophe Hervé_, Nov 17 2013, (Start)

%C Squares or double of squares that are not sum of two distinct nonzero squares.

%C Numbers without prime factor of form 4k+1 and without prime factor of form 4k+3 to an odd multiplicity.

%C The sequence is closed under multiplication. Primitive elements are 1, 2 and square of primes of form 4k+3, that is union of {1, 2} and A087691.

%C Sequence A001481 (sum of two squares) is the union of {0}, this sequence and A004431 (sum of two distinct nonzero squares). These 4 sequences are all closed under multiplication. (end)

%H Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 18 2007, <a href="/A125853/b125853.txt">Table of n, a(n) for n = 1..501</a>

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~twosquares.en.html">Two squares</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F Numbers of the form 2^e0 * 3^(2*e1) * 7^(2*e2) * 11^(2*e3) * ... * qk^(2*ek) where qk is the k-th prime of the form 4*n+3 (A002145). - Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 17 2007

%o (PARI) for(n=1,100000,fctrs=factor(n);c=1;for(i=1,matsize(fctrs)[1],p4=fctrs[i,1]%4;if(p4==1 || (p4==3 && fctrs[i,2]%2==1), c=0)); if(c,print1(n","))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 17 2007

%Y Cf. A004018, A001481, A004431.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Jan 07 2007