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.

A138317 Denominators of the squarefree totient analogs of the harmonic numbers F_n.

This page as a plain text file.
%I A138317 #11 Aug 28 2018 15:00:54
%S A138317 1,1,2,2,4,4,12,12,12,3,30,30,20,60,120,120,240,240,720,720,720,720,
%T A138317 7920,7920,7920,7920,7920,7920,55440,55440,55440,55440,55440,27720,
%U A138317 3465,3465,4620,13860,27720,27720,13860,6930,3465,3465,3465,6930,79695,79695
%N A138317 Denominators of the squarefree totient analogs of the harmonic numbers F_n.
%C A138317 F_n-H_n approaches a constant, 'kappa', conjectured to be equivalent to the difference of B_3-gamma, where B_3 is Mertens' 3rd constant and gamma is Euler's constant.
%H A138317 G. C. Greubel, <a href="/A138317/b138317.txt">Table of n, a(n) for n = 1..10000</a>
%H A138317 Dick Boland, <a href="http://www.imathination.org/kappa/kappa.pdf">An Analog of the Harmonic Numbers Over the Squarefree Integers</a>
%F A138317 a(n)=Denominator[sum(k=1 to n)mu^2(k)/phi(k)] where mu(k) is the Mobius function and phi(k) is Euler's Totient function.
%e A138317 Denominators of F_n, e.g., - F_1 = (1/1), F_2 = (1/1 + 1/1), ... F_11 = (1/1 + 1/1 + 1/2 + 0 + 1/4 + 1/2 + 1/6 + 0 + 0 + 1/4 + 1/10).
%t A138317 Table[Denominator[Sum[MoebiusMu[k]^2/EulerPhi[k], {k, 1, n}]], {n, 1, 60}]
%o A138317 (PARI) a(n) = denominator(sum(k=1, n, if (issquarefree(k), 1/eulerphi(k)))); \\ _Michel Marcus_, Aug 28 2018
%Y A138317 Cf. A138312, A138313, A138312, A138316, A138320, A138321, A083343, A001620.
%K A138317 frac,nonn
%O A138317 1,3
%A A138317 Dick Boland (abstract(AT)imathination.org), Mar 13 2008, Mar 27 2008