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A086671 Sum of floor(sqrt(d)) where d runs through the divisors of n.

%I A086671 #27 Jun 02 2022 11:11:36
%S A086671 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,
%T A086671 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,
%U A086671 23,13,14,8,34,8,14,18,23,14,25,9,21,14,25,9,37,9
%N A086671 Sum of floor(sqrt(d)) where d runs through the divisors of n.
%H A086671 T. D. Noe, <a href="/A086671/b086671.txt">Table of n, a(n) for n = 1..10000</a>
%F A086671 a(n) = Sum_{d|n} floor(sqrt(d)). - _Wesley Ivan Hurt_, Oct 25 2013
%F A086671 G.f.: sum(k>=1, floor(sqrt(k))*x^k/(1-x^k) ). - _Mircea Merca_, Feb 22 2014
%F A086671 a(n) = Sum_{i=1..floor(sqrt(n))} A135539(n,i^2). - _Ridouane Oudra_, Apr 15 2022
%e A086671 10 has divisors 1,2,5,10. floor(sqrt(d)) gives 1,1,2,3, therefore a(10)=7.
%p A086671 A086671:= proc(n)
%p A086671     add(floor(sqrt(d)), d = numtheory[divisors](n))
%p A086671 end proc; # _R. J. Mathar_, Oct 26 2013
%t A086671 Table[DivisorSum[n, Floor[Sqrt[#]] &], {n, 100}] (* _T. D. Noe_, Oct 28 2013 *)
%o A086671 (PARI) for (n=1,100,s=0; fordiv(i=n,i,s+=floor(sqrt(i))); print1(","s))
%o A086671 (PARI) a(n) = sumdiv(n, d, sqrtint(d)); \\ _Michel Marcus_, Mar 03 2020
%Y A086671 Cf. A332931, A332932, A332933, A332934, A332935.
%Y A086671 Cf. A135539.
%K A086671 nonn
%O A086671 1,2
%A A086671 _Jon Perry_, Jul 27 2003