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
Keywords
Links
- Paolo P. Lava, Table of n, a(n) for n = 1..30
Crossrefs
Subsequence of A072697. - Michel Marcus, Mar 19 2018
Programs
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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
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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 *)
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.
Comments