A027428 Number of distinct products ij with 1 <= i < j <= n. (Number of terms appearing more than once in a 1-to-n multiplication table.)

0, 1, 3, 6, 10, 13, 19, 24, 31, 36, 46, 51, 63, 70, 78, 87, 103, 111, 129, 139, 150, 161, 183, 192, 210, 223, 239, 252, 280, 291, 321, 337, 354, 371, 390, 403, 439, 458, 478, 493, 533, 549, 591, 611, 631, 654, 700, 717, 752, 774, 800, 823, 875

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Links

• Branden Aldridge, Table of n, a(n) for n = 1..20000 (terms 1..1000 from T. D. Noe).

Crossrefs

Cf. A027424, A027427, A027430.

Programs

Haskell

import Data.List (nub)
a027428 n = length $ nub [i*j | j <- [2..n], i <- [1..j-1]]
-- Reinhard Zumkeller, Jan 01 2012

Maple

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

Mathematica

a[n_] := Table[i*j, {i, 1, n-1}, {j, i+1, n}] // Flatten // Union // Length; Table[ a[n] , {n, 1, 53}] (* Jean-François Alcover, Jan 31 2013 *)

Python

def A027428(n): return len({i*j for i in range(1,n+1) for j in range(1,i)}) # Chai Wah Wu, Oct 13 2023

Formula

a(n) = A027427(n) - 1. - T. D. Noe, Jan 16 2007