OFFSET
1,2
REFERENCES
M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985, p. 103.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
FORMULA
a(n) = n +A166375(n).
For prime p>2, a(p) = (p^2+2)/3 - A228131(p)/p. In particular, for prime p==1 (mod 4), a(p) = (p^2+2)/3. - Max Alekseyev, Aug 11 2013
EXAMPLE
Row sums of the underlying triangle of floor(k^2/n), 1<=k<=n:
1;
0,2;
0,1,3;
0,1,2,4;
0,0,1,3,5;
0,0,1,2,4,6;
0,0,1,2,3,5,7;
0,0,1,2,3,4,6,8;
0,0,1,1,2,4,5,7,9;
0,0,0,1,2,3,4,6,8,10;
- R. J. Mathar, Aug 09 2013
MAPLE
A014817 := m->sum( floor(k^2/m), k=1..m);
MATHEMATICA
Table[Sum[Floor[k^2/n], {k, n}], {n, 50}] (* Harvey P. Dale, Feb 23 2015 *)
PROG
(PARI) A014817(n)=sum(k=1, n, k^2\n) \\ M. F. Hasler, Dec 11 2010
(PARI) a(n)=n^2-sum(m=1, n, sqrtint(n*m-1)) \\ Charles R Greathouse IV, Jun 20 2013
(Magma) [(&+[Floor(k^2/n): k in [1..n]]): n in [1..50]]; // G. C. Greubel, May 10 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved