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

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

Offset: 1

Author

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

Keywords

• nonn

Comments

Note that the terms are not all distinct.

Examples

			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.
		

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.

Crossrefs

Cf. A000224, A085635.

Programs

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 *)

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(tHugo Pfoertner, Aug 24 2018

Formula

a(n) = A000224(A085635(n)). - Hugo Pfoertner, Aug 24 2018

Extensions

More terms from Jud McCranie, Jul 18 2003

a(1) corrected by Hugo Pfoertner, Aug 23 2018