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A281292 Squarefree numbers that are the sum of two squares in exactly one way. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)