A332934 Sum of round(d^(3/2)) where d runs through the divisors of n.

1, 4, 6, 12, 12, 24, 20, 35, 33, 47, 37, 74, 48, 75, 75, 99, 71, 127, 84, 144, 121, 143, 111, 215, 137, 184, 173, 231, 157, 289, 174, 280, 232, 272, 238, 393, 226, 321, 297, 420, 264, 463, 283, 443, 404, 426, 323, 612, 363, 526, 440, 567, 387, 664, 456, 673

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. A058270, A086671, A332931, A332932, A332933, A332935.

Programs

Maple

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

Mathematica

Table[DivisorSum[n,Floor[1/2+Sqrt[#^3]]&],{n,80}]

Python

from math import isqrt
from sympy import divisors
def A332934(n): return sum((m:=isqrt(r:=d**3))+int(r-m*(m+1)>=1) for d in divisors(n,generator=True)) # Chai Wah Wu, Aug 03 2022