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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

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

LINKS

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

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-Fran├žois Alcover, Apr 29 2019, after Robert Israel *)

PROG

(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}

CROSSREFS

Cf. A005279.

Sequence in context: A291749 A253786 A078595 * A216513 A291437 A302231

Adjacent sequences:  A301986 A301987 A301988 * A301990 A301991 A301992

KEYWORD

nonn

AUTHOR

David A. Corneth, Mar 30 2018

STATUS

approved

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Last modified December 2 05:03 EST 2020. Contains 338865 sequences. (Running on oeis4.)