A101992 Numerator of Sum_{i=2..n} (-1)^i/(i*phi(i)).

1, 1, 11, 49, 59, 131, 559, 14533, 15289, 33031, 34417, 441877, 452173, 2224829, 9034451, 152504587, 155227307, 2932982513, 2967901397, 2945730677, 2971126229, 6189267977, 6250111487, 155668689479, 156604743479, 1404034379311, 1411857116311, 5835711932717

Offset: 2

Author

Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004

Keywords

• frac
• nonn

Comments

I conjecture that there exists a limit for Sum_{i>=2} (-1)^i/(i*phi(i)) which is ca. 0.558.

Examples

			a(4) = 11 because Sum_{i=2..4} (-1)^i/(i*phi(i)) = 1/2 - 1/6 + 1/8 = 11/24, and the numerator of 11/24 is 11.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..2296
• Eric Weisstein's World of Mathematics, Totient Function.

Crossrefs

Cf. A000010 (phi), A002618, A065484.

Programs

Mathematica

(* Generating the sum : *) f[n_Integer]/; n >= 2 := Sum[(-1)^i/(i*EulerPhi[i]), {i, 2, n}]; (* Getting the numerator: *) a[n_Integer]/; n >=2 := Numerator[f[n]]; (* Generating the sequence : *) Table[a[n], {n, 2, 20}]
Accumulate[Table[(-1)^n/(n EulerPhi[n]),{n,2,30}]]//Numerator (* Harvey P. Dale, Mar 19 2023 *)

Formula

a(n) = numerator( Sum_{i=2..n} (-1)^i/(i*phi(i)) ).

Sum_{i>=2} (-1)^i/(i*phi(i)) = 1 - (1/5) * A065484 = 0.5592286807... . - Amiram Eldar, Nov 21 2022

Extensions

More terms from Amiram Eldar, Jul 13 2019