A332932 Sum of ceiling(sqrt(d)) where d runs through the divisors of n.

1, 3, 3, 5, 4, 8, 4, 8, 6, 10, 5, 14, 5, 10, 10, 12, 6, 16, 6, 17, 11, 12, 6, 22, 9, 13, 12, 18, 7, 25, 7, 18, 13, 14, 13, 28, 8, 15, 14, 27, 8, 27, 8, 21, 20, 15, 8, 33, 11, 23, 16, 23, 9, 30, 16, 29, 16, 17, 9, 44, 9, 17, 22, 26, 17, 32, 10, 25, 17, 32, 10

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. A058268, A086671, A332931, A332933, A332934, A332935.

Programs

Maple

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

Mathematica

Table[DivisorSum[n,Ceiling[Sqrt[#]]&],{n,80}]

PARI

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

Python

from math import isqrt
from sympy import divisors
def A332932(n): return sum(1+isqrt(d-1) for d in divisors(n,generator=True)) # Chai Wah Wu, Jul 28 2022