OFFSET
1,2
COMMENTS
How can Sum_{k=1..n} floor(n^2/k^2) be expressed as a function of Sum_{k=1..n} floor(n/k)? [Ctibor O. Zizka, Feb 14 2009]
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
Benoit Cloitre, Plot of (a(n)-zeta(2)*n^2-zeta(1/2)*n)/(n^0.5/log(n))
FORMULA
From Benoit Cloitre, Jan 22 2013: (Start)
Asymptotic formula: a(n) = zeta(2)*n^2 + zeta(1/2)*n + O(n^(1/2)).
Conjecture: a(n) = zeta(2)*n^2 + zeta(1/2)*n + O(n^0.5/log(n)) (see link). (End)
EXAMPLE
a(4)=22 because floor(16/1) + floor(16/4) + floor(16/9) + floor(16,16) = 16 + 4 + 1 + 1 = 22. [Emeric Deutsch, Jan 13 2009]
MAPLE
a := proc (n) options operator, arrow: sum(floor(n^2/k^2), k = 1 .. n) end proc: seq(a(n), n = 1 .. 50); # Emeric Deutsch, Jan 13 2009
PROG
(PARI) a(n)=sum(k=1, n, n^2\k^2) \\ Benoit Cloitre, Jan 22 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, Jan 02 2009
EXTENSIONS
Definition edited by Emeric Deutsch, Jan 13 2009
Extended by Emeric Deutsch, Jan 13 2009
STATUS
approved