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%I #22 Nov 27 2022 02:09:15
%S 1,1,1,1,1,1,8,1,1,1,1,1,1,8,1,1,1,1,1,1,8,1,1,1,1,1,1,8,1,1,1,1,1,1,
%T 8,1,1,1,1,1,1,8,1,1,1,1,1,1,57,1,1,1,1,1,1,8,1,1,1,1,1,1,8,1,1,1,1,1,
%U 1,8,1,1,1,1,1,1,8,1,1,1,1,1,1,8,1,1,1,1,1,1,8,1,1,1,1,1,1,57,1,1,1,1,1,1,8
%N Denominator of the quotient sigma(7n)/sigma(n).
%C Sum of powers of 7 dividing n. - _Amiram Eldar_, Nov 27 2022
%H Amiram Eldar, <a href="/A088842/b088842.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=0} 7^k * x^(7^k) / (1 - x^(7^k)). - _Ilya Gutkovskiy_, Dec 15 2020
%F From _Amiram Eldar_, Nov 27 2022: (Start)
%F Multiplicative with a(7^e) = (7^(e+1)-1)/6, and a(p^e) = 1 for p != 7.
%F Dirichlet g.f.: zeta(s) / (1 - 7^(1 - s)).
%F 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)
%t Table[Denominator[DivisorSigma[1, 7*n]/DivisorSigma[1, n]], {n, 1, 128}] (* corrected by _Ilya Gutkovskiy_, Dec 15 2020 *)
%t a[n_] := (7^(IntegerExponent[n, 7] + 1) - 1)/6; Array[a, 100] (* _Amiram Eldar_, Nov 27 2022 *)
%o (PARI) a(n) = denominator(sigma(7*n)/sigma(n)); \\ _Michel Marcus_, Dec 15 2020
%o (PARI) a(n) = (7^(valuation(n, 7) + 1) - 1)/6; \\ _Amiram Eldar_, Nov 27 2022
%Y Cf. A000203 (sigma), A001620, A088841 (numerators), A283078 (sigma(7n)).
%Y Cf. A080278, A038712, A088837, A088838, A088839, A088840.
%K nonn,mult,frac
%O 1,7
%A _Labos Elemer_, Nov 04 2003
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