OFFSET
1,7
COMMENTS
Sum of powers of 7 dividing n. - Amiram Eldar, Nov 27 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>=0} 7^k * x^(7^k) / (1 - x^(7^k)). - Ilya Gutkovskiy, Dec 15 2020
From Amiram Eldar, Nov 27 2022: (Start)
Multiplicative with a(7^e) = (7^(e+1)-1)/6, and a(p^e) = 1 for p != 7.
Dirichlet g.f.: zeta(s) / (1 - 7^(1 - s)).
Sum_{k=1..n} a(k) ~ n*log_7(n) + (1/2 + (gamma - 1)/log(7))*n, where gamma is Euler's constant (A001620). (End)
MATHEMATICA
Table[Denominator[DivisorSigma[1, 7*n]/DivisorSigma[1, n]], {n, 1, 128}] (* corrected by Ilya Gutkovskiy, Dec 15 2020 *)
a[n_] := (7^(IntegerExponent[n, 7] + 1) - 1)/6; Array[a, 100] (* Amiram Eldar, Nov 27 2022 *)
PROG
(PARI) a(n) = denominator(sigma(7*n)/sigma(n)); \\ Michel Marcus, Dec 15 2020
(PARI) a(n) = (7^(valuation(n, 7) + 1) - 1)/6; \\ Amiram Eldar, Nov 27 2022
CROSSREFS
KEYWORD
nonn,mult,frac
AUTHOR
Labos Elemer, Nov 04 2003
STATUS
approved