cp's OEIS Frontend

A357844 Denominators of the partial alternating sums of the reciprocals of the number of divisors function (A000005).

%I A357844 #9 Oct 17 2022 01:43:23
%S A357844 1,2,1,3,6,12,12,6,2,4,4,12,12,6,12,60,60,60,60,20,5,20,20,40,120,120,
%T A357844 120,120,120,15,30,5,20,5,20,180,180,90,180,360,360,45,90,45,90,180,
%U A357844 180,180,180,180,45,90,45,360,360,45,180,45,90,180,180,45,90,630
%N A357844 Denominators of the partial alternating sums of the reciprocals of the number of divisors function (A000005).
%C A357844 See A357843 for more details.
%H A357844 László Tóth, <a href="https://www.emis.de/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1.
%F A357844 a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/d(k)), where d(k) = A000005(k).
%t A357844 Denominator[Accumulate[Array[(-1)^(# + 1)/DivisorSigma[0, #] &, 60]]]
%o A357844 (PARI) lista(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / numdiv(k); print1(denominator(s), ", "))};
%o A357844 (Python)
%o A357844 from fractions import Fraction
%o A357844 from sympy import divisor_count
%o A357844 def A357844(n): return sum(Fraction(1 if k&1 else -1, divisor_count(k)) for k in range(1,n+1)).denominator # _Chai Wah Wu_, Oct 16 2022
%Y A357844 Cf. A000005, A307704, A357843 (numerators).
%Y A357844 Similar sequences: A104529, A211178, A357821.
%K A357844 nonn,frac
%O A357844 1,2
%A A357844 _Amiram Eldar_, Oct 16 2022