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.

A161157 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 15.

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%I A161157 #8 Nov 09 2022 07:55:18
%S A161157 32767,536821761,78361756228,4397643866112,49998474112902,
%T A161157 1283800652283324,3703889238001736,36025498551189504,
%U A161157 124933950274693644,819125001391673466,1244326279702202508,10516894943504990208,10751334335850714158,60680817386182440888
%N A161157 a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 15.
%H A161157 Amiram Eldar, <a href="/A161157/b161157.txt">Table of n, a(n) for n = 1..10000</a>
%H A161157 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 A161157 From _Amiram Eldar_, Nov 08 2022: (Start)
%F A161157 a(n) = 32767 * A161025(n).
%F A161157 Sum_{k=1..n} a(k) ~ c * n^14, where c = (4681/2) * Product_{p prime} (1 + (p^13-1)/((p-1)*p^14)) =  4548.801953... .
%F A161157 Sum_{k>=1} 1/a(k) = (zeta(13)*zeta(14)/32767) * Product_{p prime} (1 - 2/p^14 + 1/p^27) = 3.05203853014...*10^(-5). (End)
%t A161157 f[p_, e_] := p^(13*e - 13) * (p^14-1) / (p-1); a[1] = 32767; a[n_] := 32767 * Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* _Amiram Eldar_, Nov 08 2022 *)
%o A161157 (PARI) a(n) = {my(f = factor(n)); 32767 * prod(i = 1, #f~, (f[i,1]^14 - 1)*f[i,1]^(13*f[i,2] - 13)/(f[i,1] - 1));} \\ _Amiram Eldar_, Nov 08 2022
%Y A161157 Cf. A000010, A013671, A013672, A161025.
%K A161157 nonn
%O A161157 1,1
%A A161157 _N. J. A. Sloane_, Nov 19 2009