A027384 Number of distinct products i*j with 0 <= i, j <= n.

1, 2, 4, 7, 10, 15, 19, 26, 31, 37, 43, 54, 60, 73, 81, 90, 98, 115, 124, 143, 153, 165, 177, 200, 210, 226, 240, 255, 268, 297, 309, 340, 355, 373, 391, 411, 424, 461, 481, 502, 518, 559, 576, 619, 639, 660, 684, 731, 748, 779, 801, 828, 851, 904, 926, 957, 979, 1009, 1039

Offset: 0

Author

Fred Schwab (fschwab(AT)nrao.edu)

Keywords

• nonn
• easy

Comments

a(n) = A027420(n,0) = A027420(n,n). - Reinhard Zumkeller, May 02 2014

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)
• R. P. Brent, C. Pomerance, D. Purdum, and J. Webster, Algorithms for the multiplication table, arXiv:1908.04251 [math.NT], 2019-2021.

Crossrefs

Equals A027424 + 1, n>0.

Cf. A027417, A027427, A027425.

Programs

Haskell

import Data.List (nub)
a027384 n = length $ nub [i*j | i <- [0..n], j <- [0..n]]
-- Reinhard Zumkeller, Jan 01 2012

Maple

A027384 := proc(n)
    local L,i,j ;
    L := {};
    for i from 0 to n do
        for j from i to n do
            L := L union {i*j};
        end do:
    end do:
    nops(L);
end proc: # R. J. Mathar, May 06 2016

Mathematica

u = {}; Table[u = Union[u, n*Range[0, n]]; Length[u], {n, 0, 100}] (* T. D. Noe, Jan 07 2012 *)

PARI

a(n) = {my(s=Set()); for (i=0, n, s = setunion(s, Set(vector(n+1, k, i*(k-1))));); #s;} \\ Michel Marcus, Jan 01 2019

Python

def A027384(n): return len({i*j for i in range(1,n+1) for j in range(1,i+1)})+1 # Chai Wah Wu, Oct 13 2023

Formula

For prime p, a(p) = a(p - 1) + p. - David A. Corneth, Jan 01 2019