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

1,2

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+=sqrtint(i)); print1(", "s))
(PARI) a(n) = sumdiv(n, d, sqrtint(d)); \\ Michel Marcus, Mar 03 2020

Crossrefs

Cf. A332931, A332932, A332933, A332934, A332935.

Cf. A135539.

Sequence in context: A274895 A173387 A133438 * A269502 A054346 A145393

Adjacent sequences: A086668 A086669 A086670 * A086672 A086673 A086674

Keyword

nonn

Author

Jon Perry, Jul 27 2003

Status

approved