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A086671 Sum of floor(sqrt(d)) where d runs through the divisors of n. 9

%I

%S 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 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 23,13,14,8,34,8,14,18,23,14,25,9,21,14,25,9,37,9

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

%H T. D. Noe, <a href="/A086671/b086671.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{d|n} floor(sqrt(d)). - _Wesley Ivan Hurt_, Oct 25 2013

%F G.f.: sum(k>=1, floor(sqrt(k))*x^k/(1-x^k) ). - _Mircea Merca_, Feb 22 2014

%e 10 has divisors 1,2,5,10. floor(sqrt(d)) gives 1,1,2,3, therefore a(10)=7.

%p A086671:= proc(n)

%p add(floor(sqrt(d)), d = numtheory[divisors](n))

%p end proc; # _R. J. Mathar_, Oct 26 2013

%t Table[DivisorSum[n, Floor[Sqrt[#]] &], {n, 100}] (* _T. D. Noe_, Oct 28 2013 *)

%o (PARI) for (n=1,100,s=0; fordiv(i=n,i,s+=floor(sqrt(i))); print1(","s))

%o (PARI) a(n) = sumdiv(n, d, sqrtint(d)); \\ _Michel Marcus_, Mar 03 2020

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

%K nonn

%O 1,2

%A _Jon Perry_, Jul 27 2003

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)