A125853 Squared radii of circles centered at a grid point in a square lattice hitting exactly 4 points. Indices k such that A004018(k)=4.

1, 2, 4, 8, 9, 16, 18, 32, 36, 49, 64, 72, 81, 98, 121, 128, 144, 162, 196, 242, 256, 288, 324, 361, 392, 441, 484, 512, 529, 576, 648, 722, 729, 784, 882, 961, 968, 1024, 1058, 1089, 1152, 1296, 1444, 1458, 1568, 1764, 1849, 1922, 1936, 2048, 2116, 2178, 2209

Offset

1,2

Comments

From Jean-Christophe Hervé, Nov 17 2013, (Start)

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

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

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.

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)

Links

Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 18 2007, Table of n, a(n) for n = 1..501

G. Xiao, Two squares

Index entries for sequences related to sums of squares

Formula

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

Prog

(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

Crossrefs

Cf. A004018, A001481, A004431.

Sequence in context: A341742 A330710 A023898 * A080025 A152111 A316856

Adjacent sequences: A125850 A125851 A125852 * A125854 A125855 A125856

Keyword

nonn

Author

Hugo Pfoertner, Jan 07 2007

Status

approved