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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.
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%I #12 Apr 29 2019 04:10:44

%S 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 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 0,2,0,4,0,0,1,0,1,1,0,3,0,0,0,5,0,0,0

%N 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 a(n) > 0 implies n is in A005279.

%H Robert Israel, <a href="/A301989/b301989.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 100: # to get a(1)..a(N)

%p V:= Vector(N):

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

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

%p for k from 1 to floor(N/(i*j)) do

%p n:= i*j*k;

%p V[n]:= V[n]+1;

%p od od od:

%p convert(V,list); # _Robert Israel_, Apr 04 2018

%t M = 100;

%t V = Table[0, {M}];

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

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

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

%t n = i j k;

%t V[[n]] = V[[n]]+1;

%t ]]];

%t V (* _Jean-François Alcover_, Apr 29 2019, after _Robert Israel_ *)

%o (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 Cf. A005279.

%K nonn

%O 1,12

%A _David A. Corneth_, Mar 30 2018