cp's OEIS Frontend

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

%I A281292 #27 Feb 10 2017 21:16:11
%S A281292 1,2,5,10,13,17,26,29,34,37,41,53,58,61,73,74,82,89,97,101,106,109,
%T A281292 113,122,137,146,149,157,173,178,181,193,194,197,202,218,226,229,233,
%U A281292 241,257,269,274,277,281,293,298,313,314,317,337,346,349,353,362,373,386,389,394,397
%N A281292 Squarefree numbers that are the sum of two squares in exactly one way.
%C A281292 Numbers of the form x^2 + y^2 with gcd(x, y) = 1 that have no other decompositions into a sum of two squares.
%C A281292 Numbers 1 and 2 together with p and 2p, where prime p == 1 (mod 4).
%C A281292 Conjecture: each positive integer is a sum |x| + |y| such that x^2 + y^2 is in the sequence.
%C A281292 Numbers in A020893 but not in A274044. - _Wolfdieter Lang_, Jan 28 2017
%H A281292 Charles R Greathouse IV, <a href="/A281292/b281292.txt">Table of n, a(n) for n = 1..10000</a>
%F A281292 a(n) ~ C n log n, where C = 4/3. - _Charles R Greathouse IV_, Feb 01 2017, corrected by _Thomas Ordowski_, Feb 10 2017
%e A281292 1 = 0^2 + 1^2 and 2 = 1^1 + 1^2.
%e A281292 p = x^2 + y^2 and 2p = (y-x)^2 + (x+y)^2.
%o A281292 (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
%Y A281292 Cf. A002144, A020893, A274044.
%K A281292 nonn,easy
%O A281292 1,2
%A A281292 _Thomas Ordowski_, Jan 19 2017