A281292 Squarefree numbers that are the sum of two squares in exactly one way.

1, 2, 5, 10, 13, 17, 26, 29, 34, 37, 41, 53, 58, 61, 73, 74, 82, 89, 97, 101, 106, 109, 113, 122, 137, 146, 149, 157, 173, 178, 181, 193, 194, 197, 202, 218, 226, 229, 233, 241, 257, 269, 274, 277, 281, 293, 298, 313, 314, 317, 337, 346, 349, 353, 362, 373, 386, 389, 394, 397

Offset

1,2

Comments

Numbers of the form x^2 + y^2 with gcd(x, y) = 1 that have no other decompositions into a sum of two squares.

Numbers 1 and 2 together with p and 2p, where prime p == 1 (mod 4).

Conjecture: each positive integer is a sum |x| + |y| such that x^2 + y^2 is in the sequence.

Numbers in A020893 but not in A274044. - Wolfdieter Lang, Jan 28 2017

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ C n log n, where C = 4/3. - Charles R Greathouse IV, Feb 01 2017, corrected by Thomas Ordowski, Feb 10 2017

Example

1 = 0^2 + 1^2 and 2 = 1^1 + 1^2.
p = x^2 + y^2 and 2p = (y-x)^2 + (x+y)^2.

Prog

(PARI) is(n)=if(n<5, n==1 || n==2, if(n%2==0, n/=2); n%4==1 && isprime(n)) \\ Charles R Greathouse IV, Feb 01 2017

Crossrefs

Cf. A002144, A020893, A274044.

Sequence in context: A224450 A226828 A020893 * A145017 A031396 A003814

Adjacent sequences: A281289 A281290 A281291 * A281293 A281294 A281295

Keyword

nonn,easy

Author

Thomas Ordowski, Jan 19 2017

Status

approved