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.
%I A215267 #61 Oct 29 2024 07:56:45
%S A215267 9,2,3,9,3,8,4,0,2,9,2,1,5,9,0,1,6,7,0,2,3,7,5,0,4,9,4,0,4,0,6,8,2,4,
%T A215267 7,2,7,6,4,5,0,2,1,6,6,8,2,7,4,4,3,6,4,4,6,3,5,1,2,3,1,9,2,4,7,7,6,2,
%U A215267 9,6,4,0,7,9,9,6,7,2,8,2,2,4,1,6,5,1,4,3,7,3,6,5,7,6,1,4,4,1,5
%N A215267 Decimal expansion of 90/Pi^4.
%C A215267 Decimal expansion of 1/zeta(4), the inverse of A013662. This is the probability that 4 randomly chosen natural numbers are relatively prime.
%C A215267 Also the asymptotic probability that a random integer is 4-free. See equivalent comments in A088453, A059956. - _Balarka Sen_, Aug 08 2012
%C A215267 The probability that the greatest common divisor of two numbers selected at random is squarefree (Christopher, 1956). - _Amiram Eldar_, May 23 2020
%D A215267 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 231.
%H A215267 Karl-Heinz Hofmann, <a href="/A215267/b215267.txt">Table of n, a(n) for n = 0..10000</a>
%H A215267 John Christopher, <a href="http://www.jstor.org/stable/2309400">The Asymptotic Density of Some k-Dimensional Sets</a>, The American Mathematical Monthly, Vol. 63, No. 6 (1956), pp. 399-401.
%H A215267 Math Forums, <a href="https://mathforums.com/threads/probability-that-a-number-is-composite.29192/page-5">Probability that a number is composite</a>, Aug 2012.
%H A215267 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A215267 Reciprocal of A013662.
%F A215267 1/zeta(4) = 90/Pi^4 = Product_{k>=1} (1 - 1/prime(k)^4) = Sum_{n>=1} mu(n)/n^4, a Dirichlet series for the Möbius function mu. See the examples in Apostol, here for s = 4. - _Wolfdieter Lang_, Aug 07 2019
%e A215267 0.92393840292159016702375049404068247276450216682744364463512319...
%t A215267 RealDigits[90/Pi^4, 10, 100][[1]] (* _Bruno Berselli_, Aug 07 2012 *)
%o A215267 (PARI) 90/Pi^4 \\ _Charles R Greathouse IV_, Aug 07 2012
%o A215267 (Maxima) 90/%pi^4; /* _Balarka Sen_, Aug 08 2012 */
%Y A215267 Cf. A013662, A046100 (4-free numbers), A059956 (1/zeta(2)).
%K A215267 nonn,cons,easy
%O A215267 0,1
%A A215267 _Jimmy Zotos_, Aug 07 2012