A362986 a(n) = A000203(A036966(n)), the sum of divisors of the n-th cubefull number A036966(n).

1, 15, 31, 40, 63, 127, 121, 156, 255, 600, 364, 511, 400, 1240, 1023, 781, 1815, 1093, 2520, 2340, 2047, 3751, 1464, 5080, 5460, 4836, 4095, 3280, 2380, 2801, 7623, 6000, 3906, 6240, 10200, 11284, 9828, 8191, 5220, 11715, 15367, 12400, 16395, 9841, 7240, 20440

Offset

1,2

Links

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

Rafael Jakimczuk and Matilde Lalín, Asymptotics of sums of divisor functions over sequences with restricted factorization structure, Notes on Number Theory and Discrete Mathematics, Vol. 28, No. 4 (2022), pp. 617-634, eq. (7).

Formula

Sum_{A036966(k) < x} a(k) = c * x^(4/3) + O(x^(113/96 + eps)), where c = A362985 * A362974 / 4 = 2.8912833599... (Jakimczuk and Lalín, 2022). [corrected Sep 21 2024]

Sum_{k=1..n} a(k) ~ c * n^4, where c = A362985 / (4 * A362974^3) = 0.006135085083... .

Mathematica

DivisorSigma[1, Select[Range[10^4], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 2 &]]

Prog

(PARI) lista(kmax) = for(k = 1, kmax, if(k==1 || vecmin(factor(k)[, 2]) > 2, print1(sigma(k), ", ")));
(Python)
from itertools import count, islice
from math import prod
from sympy import factorint
def A362986_gen(): # generator of terms
    for n in count(1):
        f = factorint(n)
        if all(e>2 for e in f.values()):
            yield prod((p**(e+1)-1)//(p-1) for p, e in f.items())
A362986_list = list(islice(A362986_gen(), 20)) # Chai Wah Wu, May 21 2023

Crossrefs

Cf. A000203, A036966, A180114, A362974, A362985.

Sequence in context: A249764 A202522 A054305 * A041442 A041440 A042017

Adjacent sequences: A362983 A362984 A362985 * A362987 A362988 A362989

Keyword

nonn

Author

Amiram Eldar, May 12 2023

Status

approved