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A086849 Sum of first n nonsquares. 6
2, 5, 10, 16, 23, 31, 41, 52, 64, 77, 91, 106, 123, 141, 160, 180, 201, 223, 246, 270, 296, 323, 351, 380, 410, 441, 473, 506, 540, 575, 612, 650, 689, 729, 770, 812, 855, 899, 944, 990, 1037, 1085, 1135, 1186, 1238, 1291, 1345, 1400, 1456, 1513, 1571, 1630 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = A000217(A000037(n)) - A000330(A000196(A000037(n))).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = SUM[from i = 1 to n] A000037(i). a(n) = SUM[from i = 1 to n] (i + [1/2 + sqrt(i)]) where [x] = floor(x). a(n) = A000217(A000037(n)) -(1/3)*(2*A000196(n)+1)*A000217(A000196(A000037(n))). - Jonathan Vos Post, Aug 28 2005

a(n) = [1/2 + (n+sqrt(n))*(n/2+sqrt(n)/6+1/3) - ([1/2 + sqrt(n)]-sqrt(n))^2*sqrt(n)] - Graeme McRae, Aug 28 2007

a(n) = n^2/2 + 2n*sqrt(n)/3 + O(n). - Charles R Greathouse IV, Aug 28 2016

MATHEMATICA

Accumulate[Table[n + Round[Sqrt[n]], {n, 120}]] (* Vladimir Joseph Stephan Orlovsky, Jul 08 2011 *)

PROG

(Haskell)

a086849 n = a086849_list !! (n-1)

a086849_list = scanl1 (+) a000037_list

-- Reinhard Zumkeller, Oct 26 2015

(PARI) a(n)=my(k=n+(sqrtint(4*n)+1)\2, s=sqrtint(k)); k*(k+1)/2 - s*(s+1)*(2*s+1)/6 \\ Charles R Greathouse IV, Aug 28 2016

CROSSREFS

Cf. A000037, A000196, A000217, A000330, A048395.

Sequence in context: A243971 A062472 A135061 * A131938 A031871 A026056

Adjacent sequences:  A086846 A086847 A086848 * A086850 A086851 A086852

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Aug 18 2003

STATUS

approved

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Last modified August 21 13:36 EDT 2017. Contains 290890 sequences.