cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A161117 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 14.

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%I A161117 #8 Nov 09 2022 07:55:27
%S A161117 16383,134193153,13059888663,549655154688,4999694820123,
%T A161117 106973548038633,264555442913583,2251387513602048,6940560290953383,
%U A161117 40952500271627493,56558559305400519,438163652766240768,413500239275072043,2166973632905158353,3985561722504070803
%N A161117 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 14.
%H A161117 Amiram Eldar, <a href="/A161117/b161117.txt">Table of n, a(n) for n = 1..10000</a>
%H A161117 Jin Ho Kwak and Jaeun Lee, <a href="https://doi.org/10.1142/9789812799890_0005">Enumeration of graph coverings, surface branched coverings and related group theory</a>, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. See p. 134.
%F A161117 From _Amiram Eldar_, Nov 08 2022: (Start)
%F A161117 a(n) = 16383 * A161010(n).
%F A161117 Sum_{k=1..n} a(k) ~ c * n^13, where c = (16383/13) * Product_{p prime} (1 + (p^12-1)/((p-1)*p^13)) = 2449.180042... .
%F A161117 Sum_{k>=1} 1/a(k) = (zeta(12)*zeta(13)/16383) * Product_{p prime} (1 - 2/p^13 + 1/p^25) = 6.1046412316...*10^(-5). (End)
%t A161117 f[p_, e_] := p^(12*e - 12) * (p^13-1) / (p-1); a[1] = 16383; a[n_] := 16383 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* _Amiram Eldar_, Nov 08 2022 *)
%o A161117 (PARI) a(n) = {my(f = factor(n)); 16383 * prod(i = 1, #f~, (f[i,1]^13 - 1)*f[i,1]^(12*f[i,2] - 12)/(f[i,1] - 1));} \\ _Amiram Eldar_, Nov 08 2022
%Y A161117 Cf. A000010, A013670, A013671, A161010.
%K A161117 nonn
%O A161117 1,1
%A A161117 _N. J. A. Sloane_, Nov 19 2009