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A071385 Number of points (i,j) on the circumference of a circle around (0,0) with squared radius A071383(n). 7
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, 6912, 7680, 8192, 9216, 10240, 11520, 12288, 13824, 15360 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Ray Chandler, Table of n, a(n) for n = 1..97

Hugo Pfoertner, Construction of A071383, A071384, A071385

FORMULA

If A071383(n)=product(p_k^e_k), k=1..klim, with p_k=k-th 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)

a(n) = 4*A000005(A071383(n)) for n>1.

a(n) = A004018(A071383(n)).

EXAMPLE

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(11) = 5^2 * 13^2 * 17^1 = 71825. Therefore A071385(11) = 4*(2+1)*(2+1)*(1+1) = 72.

CROSSREFS

Records in A004018. Cf. A071383, A071384, A300163.

Sequence in context: A311394 A172412 A212502 * A066192 A097981 A033833

Adjacent sequences:  A071382 A071383 A071384 * A071386 A071387 A071388

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, May 23 2002

STATUS

approved

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Last modified November 13 13:15 EST 2018. Contains 317149 sequences. (Running on oeis4.)