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%I #25 Mar 21 2018 11:50:26
%S 2,15,42,1365,2730,451605,870870,140645505,300690390,139098404445,
%T 304075581810,217908972526245,485155825624470,378943703223140055,
%U 1033538145201932370,1433000638322479231005,1987938667108592728530,4573285492841794762027995,12549856805456545895209890
%N Least squarefree number with n prime factors whose average is an integer.
%C A103622 lists the average values.
%C The parity of a(n) is different from the parity of n. - _David A. Corneth_, Mar 20 2018
%H Paolo P. Lava, <a href="/A300393/b300393.txt">Table of n, a(n) for n = 1..30</a>
%F a(1) = 2; 2/1 = 2;
%F a(2) = 15; (3+5)/2 = 4;
%F a(3) = 42; (2+3+7)/3 = 4;
%F a(4) = 1365; (3+5+7+13)/4 = 7;
%F a(5) = 2730; (2+3+5+7+13)/5 = 6.
%p with(combinat): P:=proc(q) local a,b,c,d,j,k,x; x:=[];
%p for j from 1 to q do x:=[op(x),ithprime(j)]; od; for j from 1 to q do
%p a:=choose(x,j); b:=10^40; d:=0;
%p for k from 1 to nops(a) do c:=convert(a[k],`+`)/j;
%p if frac(c)=0 and c<b then b:=c; d:=convert(a[k],`*`); fi; od;
%p print(d); od; end: P(30);
%t 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 *)
%Y Cf. A005117, A103622.
%Y Subsequence of A072697. - _Michel Marcus_, Mar 19 2018
%K nonn
%O 1,1
%A _Paolo P. Lava_, Mar 05 2018
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