A027427 Number of distinct products ij with 0 <= i < j <= n.

0, 1, 2, 4, 7, 11, 14, 20, 25, 32, 37, 47, 52, 64, 71, 79, 88, 104, 112, 130, 140, 151, 162, 184, 193, 211, 224, 240, 253, 281, 292, 322, 338, 355, 372, 391, 404, 440, 459, 479, 494, 534, 550, 592, 612, 632, 655, 701, 718, 753, 775, 801, 824, 876

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A027430, etc.

Cf. A027384, A027428, A027429.

Programs

Haskell

import Data.List (nub)
a027427 n = length $ nub [i*j | j <- [1..n], i <- [0..j-1]]
-- Reinhard Zumkeller, Jan 01 2012

Maple

A027427 := proc(n)
    local L, i, j ;
    L := {};
    for i from 0 to n do
        for j from i+1 to n do
            L := L union {i*j};
        end do:
    end do:
    nops(L);
end proc:  # R. J. Mathar, Jun 09 2016

Mathematica

a[n_] := Table[i*j, {i, 0, n}, {j, i+1, n}] // Flatten // Union // Length;
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Feb 03 2018 *)

Python

def A027427(n): return 1+len({i*j for i in range(1,n+1) for j in range(1,i)}) if n else 0 # Chai Wah Wu, Oct 13 2023

Formula

a(n) = A027428(n)+1. - T. D. Noe, Jan 16 2007