

A086671


Sum of floor(sqrt(d)) where d runs through the divisors of n.


8



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
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OFFSET

1,2


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = Sum_{dn} floor(sqrt(d)).  Wesley Ivan Hurt, Oct 25 2013
G.f.: sum(k>=1, floor(sqrt(k))*x^k/(1x^k) ).  Mircea Merca, Feb 22 2014


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

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



