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Record values in A002654.
3

%I #20 May 20 2021 22:49:58

%S 1,2,3,4,6,8,9,12,16,18,20,24,32,36,40,48,64,72,80,96,128,144,160,192,

%T 216,256,288,320,384,432,512,576,640,768,864,960,1024,1152,1280,1536,

%U 1728,1920,2048,2304,2560,2880,3072,3456,3840,4096,4608,5120,5760,6144

%N Record values in A002654.

%C Also numbers k such that A018782(m) > A018782(k) for all m > k.

%H Jianing Song, <a href="/A344470/b344470.txt">Table of n, a(n) for n = 1..424</a>

%F a(n) = A071385(n+1)/4.

%F a(n) = A000005(A071383(n+1)) = A002654(A071383(n+1)).

%e 9 is a term because the circle with radius sqrt(4225) centered at the origin hits exactly 4*9 = 36 integer points, and any circle with radius < sqrt(4225) centered at the origin hits fewer than 36 points.

%o (PARI) my(v=list(10^15), rec=0); for(n=1, #v, if(numdiv(v[n])>rec, rec=numdiv(v[n]); print1(rec, ", "))) \\ see program for A054994

%Y Cf. A071383, A071385, A002654, A018782, A000005, A054994.

%Y Records of Sum_{d|n} kronecker(m, d): A344472 (m=-3), this sequence (m=-4), A279542 (m=-6).

%K nonn

%O 1,2

%A _Jianing Song_, May 20 2021