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A302296 Positive numbers that can be written in exactly one way as i*j*k with i < j < 2*i. 2
6, 15, 18, 20, 28, 35, 63, 75, 77, 78, 88, 91, 99, 100, 102, 104, 110, 114, 117, 130, 138, 143, 153, 170, 174, 175, 186, 187, 189, 190, 196, 209, 221, 222, 238, 245, 246, 247, 258, 266, 272, 282, 297, 299, 304, 318, 322, 323, 325, 351, 354, 357, 366, 368, 391, 399, 402, 425, 426, 429, 437, 438 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that A301989(n)=1.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(5)=28 is in the sequence because 28 = 4*7*1 is the only way to write 28=i*j*k with i < j < 2*i.

MAPLE

N:= 1000: # to get all terms <= N

V:= Vector(N):

for i from 1 to isqrt(N-1) do

  for j from i+1 to min(floor(N/i), 2*i-1) do

    for k from 1 to floor(N/(i*j)) do

      n:= i*j*k;

      V[n]:= V[n]+1;

od od od:

select(t -> V[t]=1, [$1..N]);

MATHEMATICA

M = 1000;

V = Table[0, {M}];

For[i = 1, i <= Sqrt[M-1], i++,

  For[j = i+1, j <= Min[Floor[M/i], 2i-1], j++,

    For[k = 1, k <= Floor[M/(i j)], k++,

      n = i j k;

      V[[n]] = V[[n]]+1;

]]];

Position[V, 1] // Flatten (* Jean-Fran├žois Alcover, Apr 29 2019, after Robert Israel *)

PROG

(PARI) list(lim)=my(v=List(), u=vectorsmall(lim\=1), t); for(i=1, sqrtint(lim), for(j=i+1, min(lim\i, 2*i-1), t=i*j; forstep(n=t, lim, t, u[n]++))); for(i=1, #u, if(u[i]==1, listput(v, i))); Vec(v) \\ Charles R Greathouse IV, Apr 05 2018

CROSSREFS

Cf. A301989, A302022.

Sequence in context: A133481 A274549 A099535 * A070999 A128693 A105285

Adjacent sequences:  A302293 A302294 A302295 * A302297 A302298 A302299

KEYWORD

nonn

AUTHOR

Robert Israel, Apr 04 2018

STATUS

approved

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Last modified June 24 10:00 EDT 2019. Contains 324323 sequences. (Running on oeis4.)