A332931 Sum of round(sqrt(d)) where d runs through the divisors of n.

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

Offset: 1

Author

Harvey P. Dale, Mar 02 2020

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

a:= n-> add(round(sqrt(d)), d=numtheory[divisors](n)):
seq(a(n), n=1..80);  # Alois P. Heinz, Mar 02 2020

Mathematica

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

PARI

a(n) = sumdiv(n, d, round(sqrt(d))); \\ Michel Marcus, Mar 03 2020

Python

from math import isqrt
from sympy import divisors
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