A027429 Number of distinct products ijk with 0 <= i < j < k <= n.

0, 0, 1, 2, 5, 11, 17, 30, 43, 61, 76, 112, 127, 178, 207, 239, 275, 362, 397, 508, 555, 614, 678, 839, 884, 1005, 1093, 1199, 1278, 1530, 1591, 1882, 1999, 2134, 2276, 2433, 2519, 2922, 3097, 3279, 3392, 3885, 4015, 4564, 4751, 4939, 5187, 5841, 5988, 6423

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			a(3) = 2 (0 and 6 being the only products) and a(4) = 5 (with products 0, 6, 8, 12 and 24).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..1000 (terms 0..200 from T. D. Noe)

Crossrefs

Cf. A027425, A027426, A027427, A027430.

Programs

Haskell

import Data.List (nub)
a027429 n = length $ nub [i*j*k | k<-[2..n], j<-[1..k-1], i<-[0..j-1]]
-- Reinhard Zumkeller, Jan 01 2012

Mathematica

nn=50; prod=Table[0, {1+nn^3}]; t=Table[Do[prod[[1+i*j*k]]=1, {i,0,n}, {j,i+1,n}, {k,j+1,n}]; Count[Take[prod,1+n^3],1], {n,0,nn}] (* T. D. Noe, Jan 16 2007 *)

Python

from itertools import combinations as C
def a(n): return len(set(i*j*k for i, j, k in C(range(n+1), 3)))
print([a(n) for n in range(50)]) # Michael S. Branicky, May 28 2021

Formula

a(n) = A027430(n) + 1. - T. D. Noe, Jan 16 2007

Extensions

Corrected by T. D. Noe, Jan 16 2007