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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

%I #27 Oct 13 2023 18:50:39

%S 0,1,3,6,10,13,19,24,31,36,46,51,63,70,78,87,103,111,129,139,150,161,

%T 183,192,210,223,239,252,280,291,321,337,354,371,390,403,439,458,478,

%U 493,533,549,591,611,631,654,700,717,752,774,800,823,875

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

%H Branden Aldridge, <a href="/A027428/b027428.txt">Table of n, a(n) for n = 1..20000</a> (terms 1..1000 from T. D. Noe).

%F a(n) = A027427(n) - 1. - _T. D. Noe_, Jan 16 2007

%p 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;

%t 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 *)

%o (Haskell)

%o import Data.List (nub)

%o a027428 n = length $ nub [i*j | j <- [2..n], i <- [1..j-1]]

%o -- _Reinhard Zumkeller_, Jan 01 2012

%o (Python)

%o 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

%Y Cf. A027424, A027427, A027430.

%K nonn,easy,nice

%O 1,3

%A _N. J. A. Sloane_

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Last modified September 14 12:31 EDT 2024. Contains 375921 sequences. (Running on oeis4.)