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Sum of round(sqrt(d)) where d runs through the divisors of n.
6

%I #26 Oct 08 2022 09:45:28

%S 1,2,3,4,3,6,4,7,6,7,4,11,5,9,9,11,5,13,5,13,11,10,6,19,8,11,11,16,6,

%T 20,7,17,12,12,12,24,7,12,13,22,7,24,8,19,19,14,8,30,11,19,14,20,8,25,

%U 13,26,15,15,9,37,9,16,22,25,15,28,9,22,16,28,9,40

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

%H Amiram Eldar, <a href="/A332931/b332931.txt">Table of n, a(n) for n = 1..10000</a>

%p a:= n-> add(round(sqrt(d)), d=numtheory[divisors](n)):

%p seq(a(n), n=1..80); # _Alois P. Heinz_, Mar 02 2020

%t Table[DivisorSum[n,Floor[1/2+Sqrt[#]]&],{n,80}]

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

%o (Python)

%o from math import isqrt

%o from sympy import divisors

%o def A332931(n): return sum((m:=isqrt(d))+int(d-m*(m+1)>=1) for d in divisors(n,generator=True)) # _Chai Wah Wu_, Aug 03 2022

%Y Cf. A058267 (which has the "round" outside the sum), A086671, A332932, A332933, A332934, A332935.

%K nonn

%O 1,2

%A _Harvey P. Dale_, Mar 02 2020