A335319 Decimal expansion of Sum_{n>=2} (-1)^n/(n*phi(n)), where phi(n) is the Euler totient function A000010.

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

Offset

0,1

Comments

The formula section of A000010 provides the following conjecture: Sum_{i>=2} (-1)^i/(i*phi(i)) exists and is approximately 0.558. - Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004

A more accurate value of the conjectured limit is provided.

Links

Table of n, a(n) for n=0..86.

Formula

Equals 1 - (1/5) * A065484. - Amiram Eldar, Nov 11 2020

Example

0.5592286807124280424254343367039820674865653612424...

Prog

(PARI) 1 - prodeulerrat(1 + p/((p-1)^2*(p+1)))/5 \\ Amiram Eldar, Nov 11 2020

Crossrefs

Cf. A000010, A002618, A065484.

Sequence in context: A347682 A334383 A019843 * A046567 A199155 A243447

Adjacent sequences: A335316 A335317 A335318 * A335320 A335321 A335322

Keyword

nonn,cons

Author

Hugo Pfoertner, May 31 2020

Extensions

More terms from Amiram Eldar, Nov 11 2020

Status

approved