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

1,6

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.

Links

Table of n, a(n) for n=1..79.

Example

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.

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

Crossrefs

Cf. A077766, A077768, A077774.

Sequence in context: A352286 A352259 A245909 * A286543 A285732 A144909

Adjacent sequences: A077766 A077767 A077768 * A077770 A077771 A077772

Keyword

nonn

Author

T. D. Noe, Nov 20 2002

Status

approved