A256936 Decimal expansion of Sum_{k>=1} phi(k)/2^k, where phi is Euler's totient function.

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

Offset: 1

Author

Jean-François Alcover, Apr 13 2015

Keywords

• nonn
• cons

Examples

			1.36763080198502235079050814621308813907489199896...
		

References

• Richard K. Guy, Unsolved Problems in Number Theory, Springer, 2004, p. 139.

Links

• Paul Erdős and Ronald L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique, L'enseignement Mathématique, Université de Genève, 1980, p. 61.
• Eric Weisstein's MathWorld, Totient Function.
• Wikipedia, Euler's totient function.

Crossrefs

Cf. A000010, A007431.

Programs

Mathematica

digits = 99; m0 = 10; dd = 10; Clear[f]; f[m_] := f[m] = Sum[EulerPhi[n]/2^n, {n, 1, m}] // N[#, digits + 2*dd]&; f[m = m0] ; While[RealDigits[f[2*m], 10, digits + dd ] != RealDigits[f[m], 10, digits + dd ], m = 2*m; Print[m]]; RealDigits[f[m], 10, digits] // First

PARI

suminf(n=1,eulerphi(n)/2^n) \\ Charles R Greathouse IV, Apr 20 2016

Formula

Equals Sum_{k>=1} A007431(k)/(2^k - 1). - Amiram Eldar, Jun 23 2020