A275650 -id:A275650 - cp's OEIS frontend

A275649 Number of squarefree odd numbers k > 1 less than 10^n such that k is a sum of two squares.

2, 14, 112, 997, 8982, 82305, 764092, 7159654, 67581778, 641696858, 6122456540, 58649349611, 563729377405, 5434188304040, 52515178669973, 508607849995010

Offset: 1

Felix Fröhlich, Aug 04 2016

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

P. Shiu, Counting sums of two squares: the Meissel-Lehmer method, Mathematics of Computation, 47 (1986), 351-360.

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

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

a(7), a(11) and a(12) corrected and a(13)-a(16) added by Hiroaki Yamanouchi, Dec 25 2016

A164775 a(n) is the number of positive integers <= 10^n that can be expressed as a sum of two squares.

Original entry on oeis.org

7, 43, 330, 2749, 24028, 216341, 1985459, 18457847, 173229058, 1637624156, 15570512744, 148736628858, 1426306930865, 13722217893214, 132387263219058, 1280309691127436

Offset: 1

Eric W. Weisstein, Aug 26 2009

			a(1)=7 since 1 = 0^2 + 1^2, 2 = 1^2 + 1^2, 4 = 0^2 + 2^2, 5 = 1^2 + 2^2, 8 = 2^2 + 2^2, 9 = 0^2 + 3^2, 10 = 1^2 + 3^3.

Peter Shiu, Counting Sums of Two Squares: The Meissel-Lehmer Method, Mathematics of Computation 47:175 (July 1986), pp. 351-360. [Beware errors.]
Eric Weisstein's World of Mathematics, Landau-Ramanujan Constant

Cf. A000050, A001481, A064533, A227158, A275649, A275650.

a(n) = A180416(n) + ceiling(sqrt(10^n)). - Hiroaki Yamanouchi, Jul 14 2014

Offset changed from 0 to 1 by Robert G. Wilson v, Aug 29 2009
a(9) from Eric W. Weisstein, Aug 29 2009
a(10) from Donovan Johnson, Sep 16 2009
a(11)-a(12) from Ant King, May 02 2010
a(11)-a(12) corrected and a(13)-a(16) added by Hiroaki Yamanouchi, Jul 14 2014

cp's OEIS Frontend

A275649 Number of squarefree odd numbers k > 1 less than 10^n such that k is a sum of two squares.

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