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A334071
Decimal expansion of Sum_{k >= 1} 2^(-phi(k)), where phi is the Euler totient function (A000010).
2
2, 0, 8, 5, 5, 6, 1, 8, 8, 2, 5, 9, 7, 4, 1, 4, 6, 5, 2, 6, 3, 0, 3, 8, 7, 0, 8, 3, 2, 8, 4, 7, 4, 7, 5, 6, 1, 6, 1, 2, 1, 0, 7, 7, 6, 0, 3, 2, 3, 8, 7, 3, 7, 1, 9, 4, 7, 5, 7, 9, 3, 8, 8, 3, 1, 3, 6, 1, 8, 0, 1, 3, 3, 7, 1, 0, 5, 8, 8, 2, 1, 7, 1, 0, 3, 1, 9
OFFSET
1,1
COMMENTS
This constant is irrational (Erdős and Graham, 1980).
LINKS
Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980.
EXAMPLE
2.08556188259741465263038708328474756161210776032387...
MATHEMATICA
RealDigits[Sum[2^(-EulerPhi[n]), {n, 1, 2000}], 10, 100][[1]]
PROG
(PARI) suminf(k=1, 1/2^eulerphi(k)) \\ Michel Marcus, Apr 14 2020
CROSSREFS
Sequence in context: A321599 A020780 A377567 * A243406 A293934 A356651
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Apr 13 2020
STATUS
approved