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

1,3

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A027424, A027427, A027430.

Sequence in context: A248221 A189368 A128039 * A136850 A079248 A280774

Adjacent sequences: A027425 A027426 A027427 * A027429 A027430 A027431

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved