A077774 Number of integers between n^2 and (n+1)^2 that are the sum of two coprime squares of opposite parity; multiple representations are counted once.

0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 2, 3, 4, 3, 3, 5, 4, 4, 5, 5, 5, 5, 6, 5, 5, 7, 6, 6, 6, 8, 7, 7, 8, 9, 8, 7, 8, 9, 7, 9, 10, 7, 11, 10, 9, 10, 13, 11, 8, 11, 12, 12, 11, 11, 13, 11, 13, 12, 12, 13, 13, 13, 14, 14, 13, 14, 13, 15, 13, 15, 14, 17, 15, 14, 17, 16, 16, 16, 17, 16, 18, 18, 16, 15

Offset

1,6

Comments

See A077773 for a similar, but less restrictive sequence. A077769 counts multiple representations multiply.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

a(8)=2 because 65=64+1=49+16 and 73=64+9 are between squares 49 and 64. Note that 65 is counted only once.

Mathematica

maxN=100; lst={}; For[n=1, n<=maxN, n++, sqrs={}; 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], AppendTo[sqrs, i^2+j^2]]; j++ ]; i--; j-- ]; AppendTo[lst, Length[Union[sqrs]]]]; lst

Crossrefs

Cf. A077769, A077773.

Sequence in context: A257177 A243423 A094528 * A344150 A128219 A238969

Adjacent sequences: A077771 A077772 A077773 * A077775 A077776 A077777

Keyword

nonn

Author

T. D. Noe, Nov 20 2002

Status

approved