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A293243 Numbers that cannot be written as a product of distinct squarefree numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A100657 A245080 A212164 * A140104 A127398 A109422

Adjacent sequences:  A293240 A293241 A293242 * A293244 A293245 A293246

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 03 2017

STATUS

approved

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Last modified January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)