A334071 -id:A334071 - cp's OEIS frontend

A066781 a(n) = 2^phi(n).

2, 2, 4, 4, 16, 4, 64, 16, 64, 16, 1024, 16, 4096, 64, 256, 256, 65536, 64, 262144, 256, 4096, 1024, 4194304, 256, 1048576, 4096, 262144, 4096, 268435456, 256, 1073741824, 65536, 1048576, 65536, 16777216, 4096, 68719476736, 262144, 16777216, 65536

Offset: 1

Benoit Cloitre, Jan 18 2002

nonn

Harry J. Smith, Table of n, a(n) for n = 1..300

Cf. A000010, A334071.

Table[2^EulerPhi[n], {n, 40}] (* Arkadiusz Wesolowski, Jan 16 2013 *)

a(n) = 2^eulerphi(n); \\ Harry J. Smith, Mar 25 2010

From Amiram Eldar, Nov 18 2020: (Start)
a(n) = 2^A000010(n).
Sum_{n>=1} 1/a(n) = A334071. (End)

A334072 Decimal expansion of Sum_{k >= 1} 2^(-sigma(k)), where sigma is the sum of divisors function (A000203).

Original entry on oeis.org

7, 1, 5, 5, 5, 4, 4, 2, 2, 2, 5, 4, 9, 2, 1, 8, 6, 6, 7, 9, 8, 1, 1, 2, 4, 3, 8, 1, 9, 0, 9, 7, 9, 1, 9, 3, 3, 1, 9, 8, 6, 2, 4, 7, 1, 0, 2, 2, 1, 9, 7, 4, 9, 1, 8, 2, 5, 4, 9, 1, 2, 6, 8, 5, 6, 7, 7, 4, 8, 4, 8, 9, 4, 3, 6, 6, 4, 7, 0, 6, 1, 0, 8, 5, 5, 9, 8

Offset: 0

Amiram Eldar, Apr 13 2020

This constant is irrational (Erdős and Graham, 1980).

			0.71555442225492186679811243819097919331986247102219...

Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, L'enseignement Mathématique, Université de Genève, 1980.

Cf. A000203, A334071.

RealDigits[Sum[2^(-DivisorSigma[1, n]), {n, 1, 2000}], 10, 100][[1]]

suminf(k=1, 1/2^sigma(k)) \\ Michel Marcus, Apr 14 2020

cp's OEIS Frontend

A066781 a(n) = 2^phi(n).

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