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
Keywords
Examples
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.
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
Programs
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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
Comments