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.

A065486 Decimal expansion of Product_{p prime} (1 + 1/(p+1)^2).

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%I A065486 #17 Jan 14 2022 07:32:25
%S A065486 1,2,6,6,5,5,8,5,0,1,4,7,1,5,2,8,5,7,1,6,1,4,5,4,7,1,1,2,6,2,9,6,4,0,
%T A065486 8,4,5,3,9,5,5,6,0,2,3,5,4,5,7,3,4,4,8,2,1,1,2,1,9,6,7,3,2,9,5,4,8,3,
%U A065486 9,6,1,0,6,0,7,5,1,6,4,0,8,6,8,8,8,1,7,2,0,9,0,4,2,3,6,8,2,1,5
%N A065486 Decimal expansion of Product_{p prime} (1 + 1/(p+1)^2).
%H A065486 G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a>. [Cached copy]
%F A065486 Equals Sum_{k>=1} mu(k)^2/sigma(k)^2, where mu is the Möbius function (A008683) and sigma(k) is the sum of divisors of k (A000203). - _Amiram Eldar_, Jan 14 2022
%e A065486 1.26655850147152857161454711262964...
%t A065486 $MaxExtraPrecision = 800; digits = 99; terms = 800; P[n_] := PrimeZetaP[n]; LR = LinearRecurrence[{-3, -4, -2}, {0, 0, 2}, terms + 10]; r[n_Integer] := LR[[n]]; Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Apr 18 2016 *)
%o A065486 (PARI) prodeulerrat(1 + 1/(p+1)^2) \\ _Amiram Eldar_, Mar 15 2021
%Y A065486 Cf. A000203, A008683, A067009.
%K A065486 cons,nonn
%O A065486 1,2
%A A065486 _N. J. A. Sloane_, Nov 19 2001