The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #39 Feb 23 2020 07:28:06
%S 1,1,1,23,43,251,263,21013,1407079,4919311,818778281,2402234557,
%T 379757743297,3325743954311,54237719914087,903944329576111,
%U 46919460458733911,367421942920402841,17148430651130576323,1236225057834436760243,4190310920096832376289,535482916756698482410061
%N Minimum positive value of p_1*...*p_n*(s_1/p_1 + ... + s_n/p_n), where each s_i equals 1 or -1 and p_i is the i-th prime number.
%H Alessandro Gambini, <a href="/A332399/b332399.txt">Table of n, a(n) for n = 1..60</a> (terms 24..60 from Mattia Cafferata)
%H A. Gambini, R. Tonon and A. Zaccagnini, <a href="https://arxiv.org/abs/1911.11969">Signed harmonic sums of integers with k distinct prime factors</a>, arXiv:1911.11969 [math.NT], 2019.
%e (2*3*5*7)*(1/2 - 1/3 - 1/5 + 1/7) = (210)*(23/210) = 23, so a(4) = 23.
%t a[n_] := Block[{p = Prime@ Range@ n}, Min@ Abs[{1/p}.Transpose@ Tuples[{-1, 1}, n]] Times @@ p]; Array[a, 16] (* _Giovanni Resta_, Feb 11 2020 *)
%Y Cf. A061194 (with integers), A024530.
%K nonn
%O 1,4
%A _Alessandro Gambini_, Feb 11 2020