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

1,2

Links

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

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}]

Prog

(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

Crossrefs

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

Sequence in context: A126630 A167234 A088043 * A248376 A138796 A186970

Adjacent sequences: A332928 A332929 A332930 * A332932 A332933 A332934

Keyword

nonn

Author

Harvey P. Dale, Mar 02 2020

Status

approved