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A301989 a(n) is the number of ways to write n as i * j * k where 2 <= i <= sqrt(n), i < j <= min(2 * i - 1, floor(n / i)), k >= 1.

%I A301989 #12 Apr 29 2019 04:10:44
%S A301989 0,0,0,0,0,1,0,0,0,0,0,2,0,0,1,0,0,1,0,1,0,0,0,3,0,0,0,1,0,3,0,0,0,0,
%T A301989 1,2,0,0,0,2,0,2,0,0,2,0,0,4,0,0,0,0,0,2,0,2,0,0,0,6,0,0,1,0,0,2,0,0,
%U A301989 0,2,0,4,0,0,1,0,1,1,0,3,0,0,0,5,0,0,0
%N A301989 a(n) is the number of ways to write n as i * j * k where 2 <= i <= sqrt(n), i < j <= min(2 * i - 1, floor(n / i)), k >= 1.
%C A301989 a(n) > 0 implies n is in A005279.
%H A301989 Robert Israel, <a href="/A301989/b301989.txt">Table of n, a(n) for n = 1..10000</a>
%p A301989 N:= 100: # to get a(1)..a(N)
%p A301989 V:= Vector(N):
%p A301989 for i from 1 to isqrt(N-1) do
%p A301989   for j from i+1 to min(floor(N/i),2*i-1) do
%p A301989     for k from 1 to floor(N/(i*j)) do
%p A301989       n:= i*j*k;
%p A301989       V[n]:= V[n]+1;
%p A301989 od od od:
%p A301989 convert(V,list); # _Robert Israel_, Apr 04 2018
%t A301989 M = 100;
%t A301989 V = Table[0, {M}];
%t A301989 For[i = 1, i <= Sqrt[M-1], i++,
%t A301989   For[j = i+1, j <= Min[Floor[M/i], 2i-1], j++,
%t A301989     For[k = 1, k <= Floor[M/(i j)], k++,
%t A301989       n = i j k;
%t A301989       V[[n]] = V[[n]]+1;
%t A301989 ]]];
%t A301989 V (* _Jean-François Alcover_, Apr 29 2019, after _Robert Israel_ *)
%o A301989 (PARI) upto(n) = {my(res = vector(n)); for(i = 2, sqrtint(n), for(j = i+1, min(2 * i - 1, n \ i), for(k = 1, n \ (i * j), res[i*j*k]++))); res}
%Y A301989 Cf. A005279.
%K A301989 nonn
%O A301989 1,12
%A A301989 _David A. Corneth_, Mar 30 2018