A302296 Positive numbers that can be written in exactly one way as i*j*k with i < j < 2*i.

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

Offset: 1

Author

Robert Israel, Apr 04 2018

Keywords

• nonn

Comments

Numbers n such that A301989(n)=1.

Examples

			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.
		

Links

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

Crossrefs

Cf. A301989, A302022.

Programs

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-François Alcover, Apr 29 2019, after Robert Israel *)

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