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%I #44 Sep 05 2022 22:21:38
%S 1,4,8,12,16,24,32,36,48,64,72,80,96,128,144,160,192,256,288,320,384,
%T 512,576,640,768,864,1024,1152,1280,1536,1728,2048,2304,2560,3072,
%U 3456,3840,4096,4608,5120,6144,6912,7680,8192,9216,10240,11520,12288,13824,15360
%N Number of points (i,j) on the circumference of a circle around (0,0) with squared radius A071383(n).
%H Ray Chandler, <a href="/A071385/b071385.txt">Table of n, a(n) for n = 1..425</a>
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a071383.pdf">Construction of A071383, A071384, A071385</a>
%F 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)
%F a(n) = 4*A000005(A071383(n)) for n > 1.
%F a(n) = A004018(A071383(n)).
%F a(n) = A002654(A071383(n)) for n > 1. - _Jianing Song_, May 20 2021
%F a(n) = 4*A344470(n-1) for n > 1. - _Hugo Pfoertner_, Sep 04 2022
%e 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
%e A071383(11) = 5^2 * 13^2 * 17^1 = 71825. Therefore A071385(11) = 4*(2+1)*(2+1)*(1+1) = 72.
%o (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
%Y Records in A004018. Cf. A071383, A071384, A002144, A002654, A300163, A344470.
%K nonn
%O 1,2
%A _Hugo Pfoertner_, May 23 2002
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