A088841 Numerator of the quotient sigma(7*n)/sigma(n).

8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 400, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8, 57, 8, 8, 8, 8, 8, 8

Offset: 1

Author

Labos Elemer, Nov 04 2003

Keywords

• nonn
• easy
• frac

Links

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

Crossrefs

Cf. A088837, A088838, A088839, A088840, A088841, A088842 (denominators).

Cf. A000203, A038712, A080278, A214411, A268354, A283078.

Programs

Mathematica

Table[Numerator[DivisorSigma[1, 7*n]/DivisorSigma[1, n]], {n, 1, 128}]

PARI

a(n) = numerator(sigma(7*n)/sigma(n)); \\ Amiram Eldar, Mar 22 2024

Formula

From Amiram Eldar, Mar 22 2024: (Start)

a(n) = numerator(A283078(n)/A000203(n)).

a(n) = (7^(A214411(n)+2)-1)/6 = (49*A268354(n)-1)/6.

Sum_{k=1..n} a(k) ~ (7/log(7))*n*log(n) + (9/2 + 7*(gamma-1)/log(7))*n, where gamma is Euler's constant (A001620).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A088842(k) = 1 + 36 * Sum_{k>=1} 1/(7^k-1) = 7.87276224676... . (End)