cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A090735 Number of positive squarefree numbers <= n that can be expressed as a sum of 2 squares > 0.

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%I A090735 #14 May 08 2022 08:47:42
%S A090735 0,1,1,1,2,2,2,2,2,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,7,7,7,7,7,8,
%T A090735 8,8,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,12,12,
%U A090735 12,13,13,13,13,14,14,14,14,14,14,14,14,15,16,16,16,16,16,16,16,16,17,17
%N A090735 Number of positive squarefree numbers <= n that can be expressed as a sum of 2 squares > 0.
%D A090735 Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 100
%H A090735 Amiram Eldar, <a href="/A090735/b090735.txt">Table of n, a(n) for n = 1..10000</a>
%F A090735 a(n) is asymptotic to (6K/Pi^2)*n/sqrt(log(n)) where K is the Landau-Ramanujan constant (A064533).
%t A090735 Accumulate[Table[Boole[n > 1 && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;; , 1]], Mod[#, 4] < 3 &]], {n, 1, 100}] ] (* _Amiram Eldar_, May 08 2022 *)
%o A090735 (PARI) a(n)=sum(i=1,n,issquarefree(i)*if(sum(u=1,i,sum(v=1,u,if(u^2+v^2-i,0,1))),1,0))
%Y A090735 Cf. A005117, A020893, A064533, A090736.
%K A090735 nonn
%O A090735 1,5
%A A090735 _Benoit Cloitre_, Jan 18 2004