A027425 Number of distinct products ijk with 1 <= i,j,k <= n.

1, 4, 10, 16, 30, 40, 65, 80, 100, 120, 173, 194, 266, 301, 343, 378, 492, 536, 678, 732, 804, 876, 1075, 1130, 1247, 1343, 1450, 1537, 1833, 1909, 2248, 2362, 2515, 2668, 2850, 2940, 3400, 3587, 3789, 3919, 4477, 4624, 5242, 5440, 5654, 5916

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 200 terms from T. D. Noe)

Crossrefs

Cf. A027424, A027426, A027430.

Programs

Haskell

import Data.List (nub)
a027425 n = length $ nub [i*j*k | i <- [1..n], j <- [1..n], k <- [1..n]]
-- Reinhard Zumkeller, Jan 01 2012

Maple

f:=proc(n) local i,j,k,t1,t2; t1:={}; for i from 1 to n do for j from i to n do for k from j to n do t1:={op(t1),i*j*k}; od: od: od: t1:=convert(t1,list); nops(t1); end;

Mathematica

a[n_] := Reap[Do[Sow[i*j*k], {i, 1, n}, {j, i, n}, {k, j, n}]][[2, 1]] // Union // Length; Table[a[n], {n, 1, 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 \\ Charles R Greathouse IV, Mar 04 2014

Python

def A027425(n): return len({i*j*k for i in range(1,n+1) for j in range(1,i+1) for k in range(1,j+1)}) # Chai Wah Wu, Oct 16 2023

Formula

a(n) = A027426(n)-1. - T. D. Noe, Jan 16 2007