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A076644
a(1)=1; for n>1, a(n) = a(n-floor(sqrt(n))) + n.
3
1, 3, 6, 7, 11, 13, 18, 21, 22, 28, 32, 34, 41, 46, 49, 50, 58, 64, 68, 70, 79, 86, 91, 94, 95, 105, 113, 119, 123, 125, 136, 145, 152, 157, 160, 161, 173, 183, 191, 197, 201, 203, 216, 227, 236, 243, 248, 251, 252, 266, 278, 288, 296, 302, 306, 308, 323, 336
OFFSET
1,2
COMMENTS
a(n) = floor(2/3*n*(sqrt(n)+1)) for n in A076660.
The sign of a(n) - floor(2/3*n*(sqrt(n)+1)) changes often.
Cumulative sums of A122196. - Franklin T. Adams-Watters, Aug 25 2006
LINKS
FORMULA
Write n=r^2+s with -r < s <= r; then a(n) = r*(r+1)*(4r-1)/6 + x, where x = -s^2 if s <= 0, x = s*(2r+1-s) if s >= 0. - Dean Hickerson, Nov 11 2002
a(n) is asymptotic to 2/3*n^(3/2).
MATHEMATICA
a[n_] := Module[{r, s}, r=Floor[1/2+Sqrt[n]]; s=n-r^2; (r(r+1)(4r-1))/6+If[s<=0, -s^2, s(2r+1-s)]]
PROG
(PARI) a(n)=if(n<2, n>0, n+a(n-sqrtint(n)))
(Haskell)
a076644 n = a076644_list !! (n-1)
a076644_list = scanl1 (+) a122196_list
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Oct 23 2002
STATUS
approved