A211178 Denominator of Sum_{k=1..n}(-1)^k/phi(k), where phi = A000010.

1, 1, 2, 1, 4, 4, 12, 3, 6, 12, 60, 30, 60, 20, 40, 20, 80, 240, 720, 720, 720, 144, 1584, 1584, 7920, 7920, 7920, 7920, 55440, 55440, 11088, 5544, 27720, 55440, 55440, 55440, 55440, 6160, 18480, 2310, 9240, 9240, 3080, 3080, 1155, 210, 2415, 38640, 5520, 5520

Offset: 1

Author

Benoit Cloitre, Feb 01 2013

Keywords

• nonn
• frac

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Olivier Bordellès and Benoit Cloitre, An Alternating Sum Involving the Reciprocal of Certain Multiplicative Functions, J. Int. Seq., Vol. 16 (2013) Article #13.6.3.

Crossrefs

Cf. A000010, A082695, A211177 (numerators).

Programs

Mathematica

Denominator @ Accumulate[Table[(-1)^k/EulerPhi[k], {k, 1, 50}]] (* Amiram Eldar, Nov 20 2020 *)

PARI

a(n)=denominator(sum(k=1, n, (-1)^k/eulerphi(k)))

Formula

A211177(n)/a(n) = c*log(n) + O(1) with a suitable constant c (see ref).

The constant above is c = zeta(2)*zeta(3)/(3*zeta(6)) = (1/3) * A082695. - Amiram Eldar, Nov 20 2020

Extensions

More terms from Amiram Eldar, Nov 20 2020