A366442 The sum of divisors of the 5-rough numbers (A007310).

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

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

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

Cf. A000203, A013661, A007310, A100044, A366441.

Similar sequences: A008438, A062822, A065764, A180114, A362986, A366439, A366440.

Sequence in context: A243937 A242058 A322293 * A109138 A315858 A123303

Adjacent sequences: A366439 A366440 A366441 * A366443 A366444 A366445

Keyword

nonn,easy

Author

Amiram Eldar, Oct 10 2023

Status

approved