A332399 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.
1, 1, 1, 23, 43, 251, 263, 21013, 1407079, 4919311, 818778281, 2402234557, 379757743297, 3325743954311, 54237719914087, 903944329576111, 46919460458733911, 367421942920402841, 17148430651130576323, 1236225057834436760243, 4190310920096832376289, 535482916756698482410061
Offset: 1
Keywords
Examples
(2*3*5*7)*(1/2 - 1/3 - 1/5 + 1/7) = (210)*(23/210) = 23, so a(4) = 23.
Links
- Alessandro Gambini, Table of n, a(n) for n = 1..60 (terms 24..60 from Mattia Cafferata)
- A. Gambini, R. Tonon and A. Zaccagnini, Signed harmonic sums of integers with k distinct prime factors, arXiv:1911.11969 [math.NT], 2019.
Programs
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Mathematica
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 *)