OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{k=1..n} a(k) ~ c * n^2, where c = zeta(2) = 1.644934... (A013661).
The asymptotic mean of the abundancy index of the 5-rough numbers: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A007310(k) = Pi^2/9 = 1.0966227... (A100044).
In general, the asymptotic mean of the abundancy index of the prime(k)-rough numbers is zeta(2) * Product_{i=1..k-1} (1 - 1/prime(i)^2).
MATHEMATICA
a[n_] := DivisorSigma[1, 2*Floor[3*n/2] - 1]; Array[a, 100]
PROG
(PARI) a(n) = sigma((3*n)\2 << 1 - 1)
(Python)
from sympy import divisor_sigma
def A366442(n): return divisor_sigma((n+(n>>1)<<1)-1) # Chai Wah Wu, Oct 10 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Oct 10 2023
STATUS
approved