OFFSET
1,2
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Sum_{d|n} floor(sqrt(d)). - Wesley Ivan Hurt, Oct 25 2013
G.f.: sum(k>=1, floor(sqrt(k))*x^k/(1-x^k) ). - Mircea Merca, Feb 22 2014
a(n) = Sum_{i=1..floor(sqrt(n))} A135539(n,i^2). - Ridouane Oudra, Apr 15 2022
EXAMPLE
10 has divisors 1,2,5,10. floor(sqrt(d)) gives 1,1,2,3, therefore a(10)=7.
MAPLE
A086671:= proc(n)
add(floor(sqrt(d)), d = numtheory[divisors](n))
end proc; # R. J. Mathar, Oct 26 2013
MATHEMATICA
Table[DivisorSum[n, Floor[Sqrt[#]] &], {n, 100}] (* T. D. Noe, Oct 28 2013 *)
PROG
(PARI) for (n=1, 100, s=0; fordiv(i=n, i, s+=floor(sqrt(i))); print1(", "s))
(PARI) a(n) = sumdiv(n, d, sqrtint(d)); \\ Michel Marcus, Mar 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Jul 27 2003
STATUS
approved