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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.)
6
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
KEYWORD
nonn,easy,nice
STATUS
approved