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

Author

Hugo Pfoertner, May 31 2020

Keywords

• nonn
• cons

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.

Examples

			0.5592286807124280424254343367039820674865653612424...
		

Crossrefs

Cf. A000010, A002618, A065484.

Programs

PARI

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

Formula

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

Extensions

More terms from Amiram Eldar, Nov 11 2020