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A027430 Number of distinct products i*j*k with 1 <= i < j < k <= n.

%I A027430 #38 Feb 09 2025 18:09:32
%S A027430 0,0,1,4,10,16,29,42,60,75,111,126,177,206,238,274,361,396,507,554,
%T A027430 613,677,838,883,1004,1092,1198,1277,1529,1590,1881,1998,2133,2275,
%U A027430 2432,2518,2921,3096,3278,3391,3884,4014,4563,4750,4938,5186,5840,5987,6422,6652
%N A027430 Number of distinct products i*j*k with 1 <= i < j < k <= n.
%D A027430 Amarnath Murthy, Generalization of partition function introducing Smarandache Factor Partitions, Smarandache Notions Journal, 1-2-3, Vol. 11, 2000.
%H A027430 David A. Corneth, <a href="/A027430/b027430.txt">Table of n, a(n) for n = 1..700</a> (first 200 terms by T. D. Noe)
%H A027430 Amarnath Murthy, <a href="http://vixra.org/pdf/1403.0647v1.pdf">Generalization of partition function introducing Smarandache Factor Partitions</a>, viXra:1403.0647, 2014.
%H A027430 David A. Corneth, <a href="/A027430/a027430_1.gp.txt">Pari program</a>
%F A027430 a(n) = A027429(n)-1. - _T. D. Noe_, Jan 16 2007
%F A027430 a(n) <= A000292(n - 2). - _David A. Corneth_, Jul 31 2018
%t A027430 nn = 50;
%t A027430 prod = Table[0, {1 + nn^3}];
%t A027430 a[1] = 0;
%t A027430 a[n_] := (Do[prod[[1 + i*j*k]] = 1, {i, 0, n}, {j, i+1, n}, {k, j+1, n}]; Count[Take[prod, 1 + n^3], 1] - 1);
%t A027430 Array[a, nn] (* _Jean-François Alcover_, Jul 31 2018, after _T. D. Noe_ *)
%o A027430 (Haskell)
%o A027430 import Data.List (nub)
%o A027430 a027430 n = length $ nub [i*j*k | k<-[3..n], j<-[2..k-1], i<-[1..j-1]]
%o A027430 -- _Reinhard Zumkeller_, Jan 01 2012
%o A027430 (PARI) \\ See PARI link. _David A. Corneth_, Jul 31 2018
%o A027430 (Python)
%o A027430 def A027430(n): return len({i*j*k for i in range(1,n+1) for j in range(1,i) for k in range(1,j)}) # _Chai Wah Wu_, Oct 16 2023
%Y A027430 Cf. A000292, A027425, A088434, A100435, A100436.
%Y A027430 Number of terms in row n of A083507.
%Y A027430 Cf. A027429, A027428.
%K A027430 nonn
%O A027430 1,4
%A A027430 _N. J. A. Sloane_
%E A027430 Corrected by _David Wasserman_, Nov 18 2004