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.

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, 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, 0, 2, 0, 4, 0, 0, 1, 0, 1, 1, 0, 3, 0, 0, 0, 5, 0, 0, 0

Offset: 1

Author

David A. Corneth, Mar 30 2018

Keywords

• nonn

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005279.

Programs

Maple

N:= 100: # to get a(1)..a(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:
convert(V,list); # Robert Israel, Apr 04 2018

Mathematica

M = 100;
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;
]]];
V (* Jean-François Alcover, Apr 29 2019, after Robert Israel *)

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}