A058271 -id:A058271 - cp's OEIS frontend

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

Harvey P. Dale, Mar 02 2020

nonn

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

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

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

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

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

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

A058269 An approximation to sigma_{3/2}(n): floor( sum_{d|n} d^(3/2) ).

Original entry on oeis.org

1, 3, 6, 11, 12, 23, 19, 34, 33, 46, 37, 73, 47, 74, 75, 98, 71, 127, 83, 144, 120, 143, 111, 213, 137, 183, 173, 230, 157, 288, 173, 279, 232, 272, 237, 392, 226, 320, 296, 419, 263, 463, 282, 443, 404, 426, 323, 610, 362, 525, 440, 566, 386

Offset: 1

N. J. A. Sloane, Dec 08 2000

nonn

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

Cf. A000203, A001157, A058270, A058271, A247041.

f := proc(n) local d, t1, t2; t2 := 0; t1 := divisors(n); for d in t1 do t2 := t2 + d^(3/2) end do; t2; end proc; # exact value of sigma_{3/2}(n)

a[n_] := Floor[DivisorSigma[3/2, n]]; Array[a, 50] (* Amiram Eldar, Jan 14 2023 *)

Sum_{k=1..n} a(k) ~ (2/5)*zeta(5/2) * n^(5/2). - Amiram Eldar, Jan 14 2023

A058270 An approximation to sigma_{3/2}(n): round( sum_{d|n} d^(3/2) ).

Original entry on oeis.org

1, 4, 6, 12, 12, 24, 20, 34, 33, 47, 37, 73, 48, 75, 75, 98, 71, 127, 84, 144, 121, 144, 111, 213, 137, 183, 173, 231, 157, 289, 174, 279, 232, 272, 238, 393, 226, 321, 297, 420, 264, 463, 283, 443, 404, 426, 323, 610, 363, 525, 441, 566, 387

Offset: 1

N. J. A. Sloane, Dec 08 2000

nonn

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

Cf. A000203, A001157, A058269, A058271, A247041.

f := proc(n) local d, t1, t2; t2 := 0; t1 := divisors(n); for d in t1 do t2 := t2 + d^(3/2) end do; t2; end proc; # exact value of sigma_{3/2}(n)

a[n_] := Round[DivisorSigma[3/2, n]]; Array[a, 50] (* Amiram Eldar, Jan 14 2023 *)

Sum_{k=1..n} a(k) ~ (2/5)*zeta(5/2) * n^(5/2). - Amiram Eldar, Jan 14 2023

cp's OEIS Frontend

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

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A058269 An approximation to sigma_{3/2}(n): floor( sum_{d|n} d^(3/2) ).

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Author

Keywords

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Programs

Maple

Mathematica

Formula

A058270 An approximation to sigma_{3/2}(n): round( sum_{d|n} d^(3/2) ).

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Author

Keywords

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Crossrefs

Programs

Maple

Mathematica

Formula