A211178 - OEIS

%I #24 Dec 04 2020 11:50:43

%S 1,1,2,1,4,4,12,3,6,12,60,30,60,20,40,20,80,240,720,720,720,144,1584,

%T 1584,7920,7920,7920,7920,55440,55440,11088,5544,27720,55440,55440,

%U 55440,55440,6160,18480,2310,9240,9240,3080,3080,1155,210,2415,38640,5520,5520

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

%H Amiram Eldar, <a href="/A211178/b211178.txt">Table of n, a(n) for n = 1..10000</a>

%H Olivier Bordellès and Benoit Cloitre, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Bordelles/bord14.html">An Alternating Sum Involving the Reciprocal of Certain Multiplicative Functions</a>, J. Int. Seq., Vol. 16 (2013) Article #13.6.3.

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

%F The constant above is c = zeta(2)*zeta(3)/(3*zeta(6)) = (1/3) * A082695. - _Amiram Eldar_, Nov 20 2020

%t Denominator @ Accumulate[Table[(-1)^k/EulerPhi[k], {k, 1, 50}]] (* _Amiram Eldar_, Nov 20 2020 *)

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

%Y Cf. A000010, A082695, A211177 (numerators).

%K nonn,frac

%O 1,3

%A _Benoit Cloitre_, Feb 01 2013

%E More terms from _Amiram Eldar_, Nov 20 2020