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 A014200 Number of solutions to x^2 + y^2 <= n, excluding (0,0), divided by 4. 4
 0, 1, 2, 2, 3, 5, 5, 5, 6, 7, 9, 9, 9, 11, 11, 11, 12, 14, 15, 15, 17, 17, 17, 17, 17, 20, 22, 22, 22, 24, 24, 24, 25, 25, 27, 27, 28, 30, 30, 30, 32, 34, 34, 34, 34, 36, 36, 36, 36, 37, 40, 40, 42, 44, 44, 44, 44, 44, 46 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS From Ant King, Mar 15 2013: (Start) The terms of this sequence give a running total of the excess of the 4k + 1 divisors of the natural numbers (from 1 through to n) over their 4k + 3 divisors. To see how good the approximation n * Pi/4 is to a(n), note that a(10^6) = 785387 whereas 10^6 * Pi/4 rounds to 785398. (End) LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A014198(n) / 4. Lim_{n->inf} a(n)/n = Pi/4. a(n) = n - floor(n/3) + floor(n/5) - floor(n/7) + floor(n/9) - floor(n/11) + ... - Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 28 2003 G.f.: (1/(1 - x))*Sum_{k>=1} x^k/(1 + x^(2*k)). - Ilya Gutkovskiy, Dec 23 2016 MATHEMATICA 1/4*Prepend[SquaresR[2, #]&/@Range, 0]//Accumulate (* Ant King, Mar 15 2013 *) CROSSREFS Cf. A014198, A059851. Partial sums of A002654. Sequence in context: A055769 A162217 A123575 * A293522 A319476 A140200 Adjacent sequences:  A014197 A014198 A014199 * A014201 A014202 A014203 KEYWORD nonn AUTHOR STATUS approved

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)