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 A014198 Number of integer solutions to x^2 + y^2 <= n excluding (0,0). 5
 0, 4, 8, 8, 12, 20, 20, 20, 24, 28, 36, 36, 36, 44, 44, 44, 48, 56, 60, 60, 68, 68, 68, 68, 68, 80, 88, 88, 88, 96, 96, 96, 100, 100, 108, 108, 112, 120, 120, 120, 128, 136, 136, 136, 136, 144, 144, 144, 144, 148, 160, 160, 168, 176, 176, 176, 176, 176, 184, 184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(32)/32 = 100/32 = 3.125; lim_{n->inf} a(n)/n = Pi. The terms of this sequence are four times the running total of the excess of the 4k + 1 divisors of the natural numbers (from 1 through to n) over their 4k + 3 divisors. - Ant King, Mar 12 2013 REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 339 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Sum of Squares Function FORMULA a(n) = 4*A014200(n). a(n) = A057655(n)-1. EXAMPLE For n=2 the 8 solutions are (x,y) = (+-1,0), (0,+-1), (+-1,+-1). MAPLE A014198 := proc(n)     nops([ numtheory[thue]( abs( x^2+y^2) <= n, [ x, y ] ) ]); end proc: seq(A014198(n), n=0..60) ; MATHEMATICA Prepend[SquaresR[2, #] &/@Range[59], 0]//Accumulate (* Ant King, Mar 12 2013 *) PROG (PARI) a(n)=local(j); j=sqrtint(n); sum(x=-j, j, sum(y=-j, j, x^2+y^2<=n))-1 CROSSREFS Cf. A014200, A057655. Sequence in context: A273456 A299771 A294963 * A316316 A333288 A159786 Adjacent sequences:  A014195 A014196 A014197 * A014199 A014200 A014201 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)