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A027425 Number of distinct products ijk with 1 <= i,j,k <= n.

%I A027425 #25 Jul 08 2025 17:52:13
%S A027425 1,4,10,16,30,40,65,80,100,120,173,194,266,301,343,378,492,536,678,
%T A027425 732,804,876,1075,1130,1247,1343,1450,1537,1833,1909,2248,2362,2515,
%U A027425 2668,2850,2940,3400,3587,3789,3919,4477,4624,5242,5440,5654,5916
%N A027425 Number of distinct products ijk with 1 <= i,j,k <= n.
%H A027425 Alois P. Heinz, <a href="/A027425/b027425.txt">Table of n, a(n) for n = 1..1000</a> (first 200 terms from T. D. Noe)
%F A027425 a(n) = A027426(n)-1. - _T. D. Noe_, Jan 16 2007
%p A027425 f:=proc(n) local i,j,k,t1,t2; t1:={}; for i from 1 to n do for j from i to n do for k from j to n do t1:={op(t1),i*j*k}; od: od: od: t1:=convert(t1,list); nops(t1); end;
%t A027425 a[n_] := Reap[Do[Sow[i*j*k], {i, 1, n}, {j, i, n}, {k, j, n}]][[2, 1]] // Union // Length; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Jan 30 2018 *)
%o A027425 (Haskell)
%o A027425 import Data.List (nub)
%o A027425 a027425 n = length $ nub [i*j*k | i <- [1..n], j <- [1..n], k <- [1..n]]
%o A027425 -- _Reinhard Zumkeller_, Jan 01 2012
%o A027425 (PARI) pr(n)=my(v=List());for(i=1,n, for(j=i,n, listput(v, i*j))); Set(v)
%o A027425 a(n)=my(v=pr(n),u=v); for(i=2,n,u=Set(concat(u,v*i))); #u \\ _Charles R Greathouse IV_, Mar 04 2014
%o A027425 (Python)
%o A027425 def A027425(n): return len({i*j*k for i in range(1,n+1) for j in range(1,i+1) for k in range(1,j+1)}) # _Chai Wah Wu_, Oct 16 2023
%Y A027425 Cf. A027424, A027426, A027430.
%K A027425 nonn
%O A027425 1,2
%A A027425 _N. J. A. Sloane_