OFFSET
2,3
COMMENTS
I conjecture that there exists a limit for Sum_{i>=2} (-1)^i/(i*phi(i)) which is ca. 0.558.
LINKS
Amiram Eldar, Table of n, a(n) for n = 2..2296
Eric Weisstein's World of Mathematics, Totient Function.
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
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004
EXTENSIONS
More terms from Amiram Eldar, Jul 13 2019
STATUS
approved