A086671 Sum of floor(sqrt(d)) where d runs through the divisors of n.
1, 2, 2, 4, 3, 5, 3, 6, 5, 7, 4, 10, 4, 7, 7, 10, 5, 12, 5, 13, 8, 9, 5, 16, 8, 10, 10, 14, 6, 18, 6, 15, 10, 11, 10, 23, 7, 12, 11, 21, 7, 20, 7, 17, 16, 12, 7, 26, 10, 19, 13, 19, 8, 24, 13, 23, 13, 14, 8, 34, 8, 14, 18, 23, 14, 25, 9, 21, 14, 25, 9, 37, 9
Offset: 1
Keywords
Examples
10 has divisors 1,2,5,10. floor(sqrt(d)) gives 1,1,2,3, therefore a(10)=7.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
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Maple
A086671:= proc(n) add(floor(sqrt(d)), d = numtheory[divisors](n)) end proc; # R. J. Mathar, Oct 26 2013
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Mathematica
Table[DivisorSum[n, Floor[Sqrt[#]] &], {n, 100}] (* T. D. Noe, Oct 28 2013 *) -
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
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