A027426 Number of distinct products ijk with 0 <= i,j,k <= n.

1, 2, 5, 11, 17, 31, 41, 66, 81, 101, 121, 174, 195, 267, 302, 344, 379, 493, 537, 679, 733, 805, 877, 1076, 1131, 1248, 1344, 1451, 1538, 1834, 1910, 2249, 2363, 2516, 2669, 2851, 2941, 3401, 3588, 3790, 3920, 4478, 4625, 5243, 5441, 5655, 5917, 6647, 6799, 7197

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 201 terms from T. D. Noe)

Crossrefs

Cf. A027384, A027429.

Programs

Haskell

import Data.List (nub)
a027426 n = length $ nub [i*j*k | i <- [0..n], j <- [0..n], k <- [0..n]]
-- Reinhard Zumkeller, Jan 01 2012

Maple

a:=proc(n): nops({seq(seq(seq(i*j*k,k=0..j),j=0..i),i=0..n)}) end: seq(a(n),n=0..50); # Emeric Deutsch, Jan 25 2007

Mathematica

a[n_] := Table[i*j*k, {i, 0, n}, {j, i, n}, {k, j, n}] // Flatten // Union // Length; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jan 30 2018 *)

PARI

pr(n)=my(v=List());for(i=1,n, for(j=i,n, listput(v, i*j))); Set(v)
a(n)=my(v=pr(n),u=v); for(i=2,n,u=Set(concat(u,v*i))); #u+1 \\ Charles R Greathouse IV, Mar 04 2014

Python

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

Formula

a(n) = A027425(n) + 1. - T. D. Noe, Jan 16 2007