

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
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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[58], 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

N. J. A. Sloane


STATUS

approved



