login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300393 Least squarefree number with n prime factors whose average is an integer. 1
2, 15, 42, 1365, 2730, 451605, 870870, 140645505, 300690390, 139098404445, 304075581810, 217908972526245, 485155825624470, 378943703223140055, 1033538145201932370, 1433000638322479231005, 1987938667108592728530, 4573285492841794762027995, 12549856805456545895209890 (list; graph; refs; listen; history; text; internal format)
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 A162256

Adjacent sequences:  A300390 A300391 A300392 * A300394 A300395 A300396

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Mar 05 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)