A077769 Number of times that the sum of two coprime squares of opposite parity is an integer between n^2 and (n+1)^2; multiple representations are counted multiply.

0, 1, 1, 1, 1, 2, 2, 3, 4, 3, 2, 4, 5, 5, 3, 6, 5, 5, 7, 6, 7, 8, 9, 5, 6, 11, 7, 8, 8, 12, 9, 10, 12, 13, 11, 10, 11, 14, 11, 11, 13, 11, 17, 15, 12, 14, 18, 14, 15, 18, 18, 15, 16, 17, 18, 17, 20, 18, 19, 18, 19, 22, 20, 21, 17, 20, 21, 25, 18, 20, 23, 26, 24, 23, 23, 25, 28, 24, 24

Offset: 1

Author

T. D. Noe, Nov 20 2002

Keywords

• nonn

Comments

See A077768 for a similar, but less restrictive sequence. A077774 counts multiple representations only once. Note that by also requiring a unique representation, we obtain sequence A077766, which counts primes of the form 4k+1.

Examples

			a(8)=3 because 65=64+1, 65=49+16 and 73=64+9 are between squares 49 and 64. Note that 65 occurs twice.
		

Crossrefs

Cf. A077766, A077768, A077774.

Programs

Mathematica

maxN=100; lst={}; For[n=1, n<=maxN, n++, cnt=0; i=n; j=0; While[i>=j, j=1; While[i^2+j^2<(n+1)^2, If[i>=j&&i^2+j^2>n^2&&GCD[i, j]==1&&OddQ[i]==EvenQ[j], cnt++ ]; j++ ]; i--; j-- ]; AppendTo[lst, cnt]]; lst