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Search: id:A102548
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| A102548 |
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Number of integers <= n that are expressible in the form u^2+v^2, with u and v integers. |
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+0
1
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| 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 7, 8, 8, 8, 9, 10, 11, 11, 12, 12, 12, 12, 12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18, 19, 19, 19, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 24, 24, 25, 26, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 29, 30, 30, 30, 31, 31, 31, 31, 32, 33, 34, 34
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Daniel Shanks, The Second-Order Term in the Asymptotic Expansion of $B(x)$, Mathematics of Computation, Vol. 18, No. 85 (Jan., 1964), 75-86.
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LINKS
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Eric Weisstein's World of Mathematics, Landau-Ramanujan Constant.
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EXAMPLE
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a(8)=5 because 1=0^2+1^2, 2=1^2+1^2, 4=0^2+2^2, 5=1^2+2^2, 8=2^2+2^2, but 3,6 and 7 not are of the form u^2+v^2, with u and v integers.
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MAPLE
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a := proc(n) local aux, i, m, u, v; aux:=0; for i from 1 to n do m:=floor(sqrt(i/2)); for u from 0 to m do v:=sqrt(i-u^2); if (v = floor(v)) then aux:=aux+1; u:=m; end if; end do; end do; aux; end proc:
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CROSSREFS
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Cf. A001481, A000691.
Sequence in context: A029111 A092038 A046699 this_sequence A004001 A086841 A076502
Adjacent sequences: A102545 A102546 A102547 this_sequence A102549 A102550 A102551
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KEYWORD
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nonn
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AUTHOR
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Salvador Perez Gomez (pies314(AT)hotmail.com), Feb 24 2005
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