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

%I A302296 #17 Apr 29 2019 04:10:17
%S A302296 6,15,18,20,28,35,63,75,77,78,88,91,99,100,102,104,110,114,117,130,
%T A302296 138,143,153,170,174,175,186,187,189,190,196,209,221,222,238,245,246,
%U A302296 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
%N A302296 Positive numbers that can be written in exactly one way as i*j*k with i < j < 2*i.
%C A302296 Numbers n such that A301989(n)=1.
%H A302296 Charles R Greathouse IV, <a href="/A302296/b302296.txt">Table of n, a(n) for n = 1..10000</a>
%e A302296 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.
%p A302296 N:= 1000: # to get all terms <= N
%p A302296 V:= Vector(N):
%p A302296 for i from 1 to isqrt(N-1) do
%p A302296   for j from i+1 to min(floor(N/i),2*i-1) do
%p A302296     for k from 1 to floor(N/(i*j)) do
%p A302296       n:= i*j*k;
%p A302296       V[n]:= V[n]+1;
%p A302296 od od od:
%p A302296 select(t -> V[t]=1, [$1..N]);
%t A302296 M = 1000;
%t A302296 V = Table[0, {M}];
%t A302296 For[i = 1, i <= Sqrt[M-1], i++,
%t A302296   For[j = i+1, j <= Min[Floor[M/i], 2i-1], j++,
%t A302296     For[k = 1, k <= Floor[M/(i j)], k++,
%t A302296       n = i j k;
%t A302296       V[[n]] = V[[n]]+1;
%t A302296 ]]];
%t A302296 Position[V, 1] // Flatten (* _Jean-François Alcover_, Apr 29 2019, after _Robert Israel_ *)
%o A302296 (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
%Y A302296 Cf. A301989, A302022.
%K A302296 nonn
%O A302296 1,1
%A A302296 _Robert Israel_, Apr 04 2018