A058268 -id:A058268 - cp's OEIS frontend

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

Harvey P. Dale, Mar 02 2020

nonn

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

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

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

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

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

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

A058266 An approximation to sigma_{1/2}(n): floor( sum_{ d divides n } sqrt(d) ).

Original entry on oeis.org

1, 2, 2, 4, 3, 6, 3, 7, 5, 7, 4, 12, 4, 8, 8, 11, 5, 13, 5, 14, 9, 10, 5, 19, 8, 11, 10, 16, 6, 21, 6, 16, 11, 12, 11, 25, 7, 12, 12, 23, 7, 24, 7, 19, 18, 13, 7, 30, 10, 19, 13, 20, 8, 26, 13, 26, 14, 15, 8, 39, 8, 15, 20, 24, 14, 28, 9, 22, 15, 28, 9, 41, 9

Offset: 1

N. J. A. Sloane, Dec 08 2000

nonn

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

Cf. A000203, A001157, A058267, A058268, A078434, A086671.

with(numtheory); f := proc(n) local d, t1, t2; t2 := 0; t1 := divisors(n); for d in t1 do t2 := t2 + sqrt(d) end do; t2 end proc; # exact value of sigma_{1/2}(n)
with(numtheory):seq(floor(sigma[1/2](n)),n=1..80);

f[n_] := Floor@DivisorSigma[1/2, n]; Array[f, 73] (* Robert G. Wilson v, Aug 17 2017*)

a(n) = floor(sumdiv(n, d, sqrt(d))); \\ Michel Marcus, Aug 17 2017

Sum_{k=1..n} a(k) ~ (2/3)*zeta(3/2) * n^(3/2). - Amiram Eldar, Jan 14 2023

A058267 An approximation to sigma_{1/2}(n): round( Sum_{ d divides n } sqrt(d) ).

Original entry on oeis.org

1, 2, 3, 4, 3, 7, 4, 7, 6, 8, 4, 12, 5, 9, 9, 11, 5, 14, 5, 14, 10, 10, 6, 20, 8, 11, 11, 16, 6, 21, 7, 17, 12, 12, 12, 25, 7, 13, 13, 23, 7, 24, 8, 19, 19, 14, 8, 31, 11, 20, 14, 20, 8, 26, 14, 26, 15, 15, 9, 39, 9, 16, 21, 25, 15, 28, 9, 23, 16, 28, 9, 42, 10

Offset: 1

N. J. A. Sloane, Dec 08 2000

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000203, A001157, A058266, A058268, A078434.

map(round @ numtheory:-sigma[1/2], [$1..100]); # Robert Israel, Aug 18 2017

f[n_] := Round@ DivisorSigma[1/2, n]; Array[f, 70] (* Robert G. Wilson v, Aug 17 2017 *)

a(n) = round(sumdiv(n, d, sqrt(d))); \\ Michel Marcus, Aug 17 2017

Sum_{k=1..n} a(k) ~ (2/3)*zeta(3/2) * n^(3/2). - Amiram Eldar, Jan 14 2023

cp's OEIS Frontend

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

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A058266 An approximation to sigma_{1/2}(n): floor( sum_{ d divides n } sqrt(d) ).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A058267 An approximation to sigma_{1/2}(n): round( Sum_{ d divides n } sqrt(d) ).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula