A300393 Least squarefree number with n prime factors whose average is an integer.

2, 15, 42, 1365, 2730, 451605, 870870, 140645505, 300690390, 139098404445, 304075581810, 217908972526245, 485155825624470, 378943703223140055, 1033538145201932370, 1433000638322479231005, 1987938667108592728530, 4573285492841794762027995, 12549856805456545895209890

Offset

1,1

Comments

A103622 lists the average values.

The parity of a(n) is different from the parity of n. - David A. Corneth, Mar 20 2018

Links

Paolo P. Lava, Table of n, a(n) for n = 1..30

Formula

a(1) = 2; 2/1 = 2;

a(2) = 15; (3+5)/2 = 4;

a(3) = 42; (2+3+7)/3 = 4;

a(4) = 1365; (3+5+7+13)/4 = 7;

a(5) = 2730; (2+3+5+7+13)/5 = 6.

Maple

with(combinat): P:=proc(q) local a, b, c, d, j, k, x; x:=[];
for j from 1 to q do x:=[op(x), ithprime(j)]; od; for j from 1 to q do
a:=choose(x, j); b:=10^40; d:=0;
for k from 1 to nops(a) do c:=convert(a[k], `+`)/j;
if frac(c)=0 and c<b then b:=c; d:=convert(a[k], `*`); fi; od;
print(d); od; end: P(30);

Mathematica

f[n_] := If[n == 0, {1}, Block[{P = Product[Prime@ i, {i, n}], lim, k = 1, c, w = ConstantArray[1, n]}, lim = Prime[n + 1] P; {w}~Join~Reap[Do[w = If[k == 1, MapAt[# + 1 &, w, -k], Join[Drop[MapAt[# + 1 &, w, -k], -k + 1], ConstantArray[1, k - 1]]]; c = Times @@ Map[If[# == 0, 1, Prime@ #] &, Accumulate@ w]; If[c < lim, Sow[w]; k = 1, If[k == n, Break[], k++]], {i, Infinity}]][[-1, 1]]]]; Array[Min@ Map[Times @@ # &, Select[Map[Prime@ Accumulate@ # &, f@ #], IntegerQ@ Mean@ # &]] &, 14] (* Michael De Vlieger, Mar 19 2018 *)

Crossrefs

Cf. A005117, A103622.

Subsequence of A072697. - Michel Marcus, Mar 19 2018

Sequence in context: A032016 A254856 A001007 * A152015 A318914 A346546

Adjacent sequences: A300390 A300391 A300392 * A300394 A300395 A300396

Keyword

nonn

Author

Paolo P. Lava, Mar 05 2018

Status

approved