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 A371133 #7 Mar 12 2024 02:48:45
%S A371133 2,4,8,1,0,6,1,0,1,9,7,9,0,7,6,2,6,9,7,9,3,7,4,4,7,6,9,6,3,9,8,6,5,7,
%T A371133 3,9,5,6,8,6,8,9,7,7,6,1,2,1,7,1,3,1,6,2,0,7,2,3,6,9,3,3,7,1,7,5,5,2,
%U A371133 0,4,4,1,0,9,0,9,3,0,3,3,3,6,9,2,6,7,2,0,2,4,8,3,2,4,7,1,2,9,3,8,4,8,6,4,4
%N A371133 Decimal expansion of Sum_{n>=1} d(n)/n!, where d(n) is the number of divisors of n.
%C A371133 This constant is irrational (Erdős and Straus, 1971).
%H A371133 Paul Erdős and Ernst G. Straus, <a href="http://dx.doi.org/10.2140/pjm.1971.36.635">Some number theoretic results</a>, Pacific Journal of Mathematics, Vol. 36, No. 3 (1971), pp. 635-646.
%H A371133 Michael Ian Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/Overcounting.pdf">Overcounting Functions</a>, 2011.
%F A371133 Equals Sum_{j,k>=1} 1/(j*k)! (Shamos, 2011, p. 4).
%e A371133 2.48106101979076269793744769639865739568689776121713...
%p A371133 with(numtheory); evalf(Sum(tau(n)/factorial(n), n = 1 .. infinity), 120)
%t A371133 RealDigits[N[Sum[DivisorSigma[0, n]/n!, {n, 1, 500}], 120]][[1]]
%o A371133 (PARI) suminf(k=1,numdiv(k)/k!)
%Y A371133 Cf. A000005, A336334.
%Y A371133 Sum_{n>=1} sigma_k(n)/n!: this sequence (k=0), A227988 (k=1), A227989 (k=2), A307036 (k=3), A359060 (k=4).
%K A371133 nonn,cons
%O A371133 1,1
%A A371133 _Amiram Eldar_, Mar 12 2024