A293243 Numbers that cannot be written as a product of distinct squarefree numbers.

4, 8, 9, 16, 24, 25, 27, 32, 40, 48, 49, 54, 56, 64, 72, 80, 81, 88, 96, 104, 108, 112, 121, 125, 128, 135, 136, 144, 152, 160, 162, 169, 176, 184, 189, 192, 200, 208, 216, 224, 232, 240, 243, 248, 250, 256, 272, 288, 289, 296, 297, 304, 320, 324, 328, 336

Offset

1,1

Comments

First differs from A212164 at a(441).

Numbers n such that A050326(n) = 0. - Felix Fröhlich, Oct 04 2017

Includes A246547, and all numbers of the form p^a*q^b where p and q are primes, a >= 1 and b >= 3. - Robert Israel, Oct 10 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

120 is not in the sequence because 120 = 2*6*10. 3600 is not in the sequence because 3600 = 2*6*10*30.

Maple

N:= 1000: # to get all terms <= N
A:= Vector(N):
A[1]:= 1:
for n from 2 to N do
  if numtheory:-issqrfree(n) then
      S:= [$1..N/n]; T:= n*S; A[T]:= A[T]+A[S]
    fi;
od:
select(t -> A[t]=0, [$1..N]); # Robert Israel, Oct 10 2017

Mathematica

nn=500;
sqfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sqfacs[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], SquareFreeQ]}]];
Select[Range[nn], Length[sqfacs[#]]===0&]

Crossrefs

Cf. A001055, A005117, A045778, A050320, A050326, A246547, A292432, A292444.

Sequence in context: A361204 A245080 A212164 * A339740 A345171 A335448

Adjacent sequences: A293240 A293241 A293242 * A293244 A293245 A293246

Keyword

nonn

Author

Gus Wiseman, Oct 03 2017

Status

approved