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Search: id:A071385
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| A071385 |
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Number of points (i,j) on the circumference of a circle around (0,0) with squared radius A071383(n). |
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7
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| 1, 4, 8, 12, 16, 24, 32, 36, 48, 64, 72, 80, 96, 128, 144, 160, 192, 256, 288, 320, 384, 512, 576, 640, 768, 864, 1024, 1152, 1280, 1536, 1728, 2048, 2304, 2560, 3072, 3456, 3840, 4096, 4608, 5120, 6144
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Hugo Pfoertner, Construction of A071383, A071384, A071385
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FORMULA
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If A071383(n)=product(p_k^e_k), k=1..klim, with p_k=kth prime of the form 4*i+1 and e_1 >= e_2 >= .. >= e_klim > 0 then A071385(n)=4*product(e_k+1), k=1..klim. (J. H. Conway)
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EXAMPLE
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Circles with radius 1 and 2 have 4 lattice points on their circumference, so a(1)=4. A circle with radius sqrt(5) passes through 8 lattice points of the shape (2,1), so a(2)=8. A circle with radius 5 passes through 4 lattice points of shape (5,0) and through 8 points of shape (4,3), so a(3)=4+8=12
A071383(10) = 5^2 * 13^2 * 17^1 = 71825. Therefore A071385(10) = 4*(2+1)*(2+1)*(1+1) = 72.
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CROSSREFS
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Cf. A071383, A071384.
Sequence in context: A109238 A102861 A004976 this_sequence A066192 A097981 A033833
Adjacent sequences: A071382 A071383 A071384 this_sequence A071386 A071387 A071388
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), May 23 2002
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