A083508 Number of distinct products i*j*k with 1 <= i < j <= k <= n and j < n.

0, 0, 2, 7, 16, 24, 40, 56, 77, 96, 137, 158, 214, 249, 284, 322, 418, 464, 583, 645, 708, 774, 946, 1007, 1125, 1220, 1330, 1420, 1685, 1768, 2069, 2203, 2346, 2492, 2658, 2750, 3166, 3362, 3553, 3675, 4183, 4344, 4909, 5129, 5327, 5575, 6252, 6432, 6849

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A027430, A100435.

Programs

Maple

V:= Vector(100):
S:= {}:
for n from 1 to 100 do
  S:= S union {seq(i*(n-1)^2, i=1..n-2), seq(seq(i*j*n, i=1..j-1),j=2..n-1)};
  V[n]:= nops(S);
od:
convert(V,list); # Robert Israel, Aug 03 2025

PARI

for(n=1,100,s=Set();for(i=1,n-2,for(j=i+1,n-1,for(k=j,n,p=i*j*k;if(!setsearch(s,p),s=setunion(s,Set(p))))));print1(length(s),",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 06 2006

Extensions

Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 06 2006

Definition corrected by Robert Israel, Aug 03 2025