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

1,4

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.

Example

(2*3*5*7)*(1/2 - 1/3 - 1/5 + 1/7) = (210)*(23/210) = 23, so a(4) = 23.

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 *)

Crossrefs

Cf. A061194 (with integers), A024530.

Sequence in context: A180534 A138975 A168439 * A198949 A334113 A214891

Adjacent sequences: A332396 A332397 A332398 * A332400 A332401 A332402

Keyword

nonn

Author

Alessandro Gambini, Feb 11 2020

Status

approved