cp's OEIS Frontend

A097269 Numbers that are the sum of two nonzero squares but not the difference of two nonzero squares.

%I A097269 #19 Feb 16 2025 08:32:54
%S A097269 2,10,18,26,34,50,58,74,82,90,98,106,122,130,146,162,170,178,194,202,
%T A097269 218,226,234,242,250,274,290,298,306,314,338,346,362,370,386,394,410,
%U A097269 442,450,458,466,482,490,514,522,530,538,554,562,578,586,610,626,634
%N A097269 Numbers that are the sum of two nonzero squares but not the difference of two nonzero squares.
%C A097269 Intersection of A000404 (sum of squares) and complement of A024352 (difference of squares).
%C A097269 Numbers of the form 4k+2 = double of an odd number, with the odd number equal to the sum of 2 squares (sequence A057653). - _Jean-Christophe Hervé_, Oct 24 2015
%C A097269 Numbers that are the sum of two odd squares. - _Jean-Christophe Hervé_, Oct 25 2015
%H A097269 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SumofSquaresFunction.html">Sum of Squares Function.</a>
%e A097269 2 = 1^2 + 1^2, 10 = 1^2 + 3^2, 18 = 3^2 + 3^2.
%o A097269 (PARI) is(n)=if(n%4!=2,return(0)); my(f=factor(n/2)); for(i=1,#f[,1],if(bitand(f[i,2],1)==1&&bitand(f[i,1],3)==3, return(0))); 1 \\ _Charles R Greathouse IV_, May 31 2013
%o A097269 (Python)
%o A097269 from itertools import count, islice
%o A097269 from sympy import factorint
%o A097269 def A097269_gen(): # generator of terms
%o A097269     return filter(lambda n:all(p & 3 != 3 or e & 1 == 0 for p, e in factorint(n//2).items()),count(2,4))
%o A097269 A097269_list = list(islice(A097269_gen(),30)) # _Chai Wah Wu_, Jun 28 2022
%Y A097269 Cf. A000404, A024352, A097268, A097270, A097271. Equals twice A057653.
%Y A097269 Cf. A020668, A263715.
%K A097269 nonn
%O A097269 1,1
%A A097269 _Ray Chandler_, Aug 19 2004