OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Rafael Jakimczuk and Matilde LalĂn, 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. (8).
FORMULA
Sum_{A036966(k) < x} a(k) = c_1 * x^(1/3) * log(x)^3 + c_2 * x^(1/3) * log(x)^2 + c_3 * x^(1/3) * log(x) + c_4 * x^(1/3) + O(x^(7/24 + eps)), where c_1, c_2, c_3 and c_4 are constants. c_1 = Product_{p prime} ((1-1/p)^4 * (1 + 1/((p^(1/3) - 1)^2*p^(1/3)) + 3/(p-p^(2/3))))/162 = 0.1346652397135839416... . [corrected Sep 21 2024]
MATHEMATICA
DivisorSigma[0, Select[Range[25000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 2 &]]
PROG
(PARI) lista(kmax) = for(k = 1, kmax, if(k==1 || vecmin(factor(k)[, 2]) > 2, print1(numdiv(k), ", ")));
(Python)
from itertools import count, islice
from math import prod
from sympy import factorint
def A363195_gen(): # generator of terms
for n in count(1):
f = factorint(n).values()
if all(e>2 for e in f):
yield prod(e+1 for e in f)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, May 21 2023
STATUS
approved