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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.
2
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.
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Nov 20 2002
STATUS
approved