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A101992
Numerator of Sum_{i=2..n} (-1)^i/(i*phi(i)).
2
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
2,3
COMMENTS
I conjecture that there exists a limit for Sum_{i>=2} (-1)^i/(i*phi(i)) which is ca. 0.558.
LINKS
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
Cf. A000010 (phi), A002618, A065484.
Sequence in context: A211058 A239460 A226676 * A356792 A160671 A297521
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