A332935 Sum of ceiling(n^(3/2)) where d runs through the divisors of n.

1, 4, 7, 12, 13, 25, 20, 35, 34, 48, 38, 75, 48, 76, 78, 99, 72, 129, 84, 146, 123, 145, 112, 216, 138, 184, 175, 233, 158, 293, 174, 281, 234, 274, 240, 395, 227, 322, 298, 422, 264, 467, 283, 445, 407, 427, 324, 613, 363, 527, 443, 567, 387, 667, 458, 676

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. A058271, A086671, A332931, A332932, A332933, A332934.

Programs

Maple

a:= n-> add(ceil(d^(3/2)), d=numtheory[divisors](n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Mar 02 2020

Mathematica

Table[DivisorSum[n,Ceiling[Sqrt[#^3]]&],{n,80}]

PARI

a(n)={sumdiv(n, d, 1 + sqrtint(d^3 - 1))} \\ Andrew Howroyd, Mar 02 2020

Python

from math import isqrt
from sympy import divisors
def A332935(n): return sum(1+isqrt(d**3-1) for d in divisors(n,generator=True)) # Chai Wah Wu, Aug 03 2022