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A071385
Number of points (i,j) on the circumference of a circle around (0,0) with squared radius A071383(n).
11
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
OFFSET
1,2
FORMULA
a(n) = 4 * Product_{k=1..klim} (e_k + 1), where klim and e_1 >= e_2 >= ... >= e_klim > 0 are known from A071383(n) = Product_{k=1..klim} p_k^e_k, with p_k = k-th prime of the form 4i+1. (J. H. Conway)
a(n) = 4*A000005(A071383(n)) for n > 1.
a(n) = A004018(A071383(n)).
a(n) = A002654(A071383(n)) for n > 1. - Jianing Song, May 20 2021
a(n) = 4*A344470(n-1) for n > 1. - Hugo Pfoertner, Sep 04 2022
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.
PROG
(PARI) my(v=list(10^15), rec=0); print1(1, ", "); for(n=1, #v, if(numdiv(v[n])>rec, rec=numdiv(v[n]); print1(4*rec, ", "))) \\ Jianing Song, May 20 2021, see program for A054994
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, May 23 2002
STATUS
approved