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A366442
The sum of divisors of the 5-rough numbers (A007310).
2
1, 6, 8, 12, 14, 18, 20, 24, 31, 30, 32, 48, 38, 42, 44, 48, 57, 54, 72, 60, 62, 84, 68, 72, 74, 96, 80, 84, 108, 90, 112, 120, 98, 102, 104, 108, 110, 114, 144, 144, 133, 156, 128, 132, 160, 138, 140, 168, 180, 150, 152, 192, 158, 192, 164, 168, 183, 174, 248
OFFSET
1,2
LINKS
FORMULA
a(n) = A000203(A007310(n)).
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