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 A084848 a(n) is the number of quadratic residues of A085635(n). 6
 1, 2, 2, 3, 4, 4, 7, 8, 12, 14, 16, 16, 24, 28, 32, 42, 48, 48, 48, 64, 84, 96, 112, 144, 144, 176, 192, 192, 288, 336, 336, 504, 576, 576, 704, 864, 1008, 1056, 1152, 1232, 1152, 1344, 1728, 1920, 2016, 2016, 2352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Note that the terms are not all distinct. LINKS Keith F. Lynch, Table of n, a(n) for n = 1..200 (first 111 terms from Hugo Pfoertner). Andreas Enge, William Hart, Fredrik Johansson, Short addition sequences for theta functions, arXiv:1608.06810 [math.NT], 2016-2018. FORMULA a(n) = A000224(A085635(n)). - Hugo Pfoertner, Aug 24 2018 EXAMPLE 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. MATHEMATICA 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]], #][[1]] ]] &, Union@ FoldList[Max, t[[All, 1]] ] ] ] (* Michael De Vlieger, Sep 10 2018 *) PROG (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 r=2; for(k=1, 1e6, v=a000224(k); t=v/k; if(t

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Last modified April 8 14:15 EDT 2020. Contains 333314 sequences. (Running on oeis4.)