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_{A001694(k) < x} a(k) = c_1 * sqrt(x) * log(x)^2 + c_2 * sqrt(x) * log(x) + c_3 * sqrt(x) + O(x^(5/12 + eps)), where c_1, c_2 and c_3 are constants. c_1 = Product_{p prime} (1 + 4/p^(3/2) - 1/p^2 - 6/p^(5/2) + 2/p^(7/2))/8 = 0.516273682988566836609... . [corrected Sep 21 2024]
MATHEMATICA
DivisorSigma[0, Select[Range[3000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]]
PROG
(PARI) apply(numdiv, select(ispowerful, [1..3000]))
(Python)
from itertools import count, islice
from math import prod
from sympy import factorint
def A363194_gen(): # generator of terms
for n in count(1):
f = factorint(n).values()
if all(e>1 for e in f):
yield prod(e+1 for e in f)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, May 21 2023
STATUS
approved