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A088841
Numerator of the quotient sigma(7*n)/sigma(n).
4
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
1,1
LINKS
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)
MATHEMATICA
Table[Numerator[DivisorSigma[1, 7*n]/DivisorSigma[1, n]], {n, 1, 128}]
PROG
(PARI) a(n) = numerator(sigma(7*n)/sigma(n)); \\ Amiram Eldar, Mar 22 2024
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Labos Elemer, Nov 04 2003
STATUS
approved