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 A084848 a(n) is the number of quadratic residues of A085635(n). 6

%I

%S 1,2,2,3,4,4,7,8,12,14,16,16,24,28,32,42,48,48,48,64,84,96,112,144,

%T 144,176,192,192,288,336,336,504,576,576,704,864,1008,1056,1152,1232,

%U 1152,1344,1728,1920,2016,2016,2352

%N a(n) is the number of quadratic residues of A085635(n).

%C Note that the terms are not all distinct.

%H Keith F. Lynch, <a href="/A084848/b084848.txt">Table of n, a(n) for n = 1..200</a> (first 111 terms from Hugo Pfoertner).

%H Andreas Enge, William Hart, Fredrik Johansson, <a href="http://arxiv.org/abs/1608.06810">Short addition sequences for theta functions</a>, arXiv:1608.06810 [math.NT], 2016-2018.

%F a(n) = A000224(A085635(n)). - _Hugo Pfoertner_, Aug 24 2018

%e a(2)=2 because there are 2 different quadratic residues modulo 3, so 3 has 66.67% of quadratic residues density, while 2 has a 100%, so 3 has the least quadratic residues density up to 3.

%t Block[{s = Range[0, 2^15 + 1]^2, t}, t = Array[{#1/#2, #2} & @@ {#, Length@ Union@ Mod[Take[s, # + 1], #]} &, Length@ s - 1]; Map[t[[All, -1]][[FirstPosition[t[[All, 1]], #][] ]] &, Union@ FoldList[Max, t[[All, 1]] ] ] ] (* _Michael De Vlieger_, Sep 10 2018 *)

%o (PARI) a000224(n)=my(f=factor(n));prod(i=1,#f[,1],if(f[i,1]==2,2^f[1,2]\6+2,f[i,1]^(f[i,2]+1)\(2*f[i,1]+2)+1)) \\ from _Charles R Greathouse IV_

%o r=2;for(k=1,1e6,v=a000224(k);t=v/k;if(t<r,r=t;print1(v, ", "))) \\ _Hugo Pfoertner_, Aug 24 2018

%Y Cf. A000224, A085635.

%K nonn

%O 1,2

%A Jose R. Brox (tautocrona(AT)terra.es), Jul 12 2003

%E More terms from _Jud McCranie_, Jul 18 2003

%E a(1) corrected by _Hugo Pfoertner_, Aug 23 2018

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Last modified October 23 22:49 EDT 2019. Contains 328378 sequences. (Running on oeis4.)