login
Number of squarefree odd numbers k > 1 less than 10^n such that k is a sum of two squares.
3

%I #22 Dec 25 2016 12:08:53

%S 2,14,112,997,8982,82305,764092,7159654,67581778,641696858,6122456540,

%T 58649349611,563729377405,5434188304040,52515178669973,508607849995010

%N Number of squarefree odd numbers k > 1 less than 10^n such that k is a sum of two squares.

%C This sequence gives the values of the counting function U(x), whose values are given in table 2 on page 359 of Shiu, 1986.

%H P. Shiu, <a href="http://dx.doi.org/10.1090/S0025-5718-1986-0842141-1">Counting sums of two squares: the Meissel-Lehmer method</a>, Mathematics of Computation, 47 (1986), 351-360.

%t Table[Count[Range[1, 10^n, 2], k_ /; SquareFreeQ@ k && SquaresR[2, k] > 0], {n, 6}] (* _Michael De Vlieger_, Aug 04 2016 *)

%Y Cf. A164775: W(x), A275650: V(x).

%K nonn,more

%O 1,1

%A _Felix Fröhlich_, Aug 04 2016

%E a(7), a(11) and a(12) corrected and a(13)-a(16) added by _Hiroaki Yamanouchi_, Dec 25 2016