cp's OEIS Frontend

A379362 Denominators of the partial alternating sums of the reciprocals of the number of abelian groups function (A000688).

%I A379362 #7 Dec 22 2024 16:52:55
%S A379362 1,1,1,2,2,2,2,6,3,3,3,6,6,6,6,30,30,15,15,30,30,30,30,30,15,15,15,30,
%T A379362 30,30,30,210,210,210,210,420,420,420,420,420,420,420,420,420,420,420,
%U A379362 420,420,420,420,420,420,420,140,140,420,420,420,420,420,420,420
%N A379362 Denominators of the partial alternating sums of the reciprocals of the number of abelian groups function (A000688).
%H A379362 Amiram Eldar, <a href="/A379362/b379362.txt">Table of n, a(n) for n = 1..10000</a>
%H A379362 László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.8, pp. 27-28.
%F A379362 a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A000688(k)).
%t A379362 Denominator[Accumulate[Table[(-1)^(n+1)/FiniteAbelianGroupCount[n], {n, 1, 100}]]]
%o A379362 (PARI) f(n) = vecprod(apply(numbpart, factor(n)[, 2]));
%o A379362 list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / f(k); print1(denominator(s), ", "))};
%Y A379362 Cf. A000688, A063966, A370897, A379360, A379361 (numerators).
%K A379362 nonn,easy,frac
%O A379362 1,4
%A A379362 _Amiram Eldar_, Dec 21 2024