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Search: id:A077774
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| A077774 |
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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. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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See A077773 for a similar, but less restrictive sequence. A077769 counts multiple represenations multiply.
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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Cf. A077769, A077773.
Sequence in context: A098014 A059957 A094528 this_sequence A128219 A116505 A110534
Adjacent sequences: A077771 A077772 A077773 this_sequence A077775 A077776 A077777
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 20 2002
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