|
%I #9 Jul 05 2021 15:08:10
%S 1,9,5,4,0,8,5,3,5,7,8,7,6,0,0,6,2,1,3,1,4,4,5,9,4,8,6,1,1,4,7,1,4,9,
%T 5,4,0,3,7,0,6,7,2,7,7,0,1,8,6,9,6,1,0,6,0,8,2,9,8,7,7,7,2,0,7,8,8,7,
%U 0,8,7,9,8,5,5,2,7,6,0,9,2,3,7,9,0
%N Decimal expansion of Sum_{n>=1} phi(n)/n!, where phi(n) is the Euler totient function A000010.
%C The following comment is provided in A000010: Sum_{n>=1} a(n)/n! = 1.954085357876006213144... This sum is referenced in Plouffe's inverter. - _Alexander R. Povolotsky_, Feb 02 2013
%C This constant is irrational (Erdős and Straus, 1974). - _Amiram Eldar_, Jul 04 2021
%H Paul Erdős and Ernst G. Straus, <a href="http://dx.doi.org/10.2140/pjm.1974.55.85">On the irrationality of certain series</a>, Pacific journal of mathematics, Vol. 55, No. 1 (1974), pp. 85-92.
%e 1.9540853578760062131445948611471495403706727701869610608298777207887...
%o (PARI) suminf(k=1,eulerphi(k)/k!)
%Y Cf. A000010.
%K nonn,cons
%O 1,2
%A _Hugo Pfoertner_, Jul 22 2020
|
