cp's OEIS Frontend

A083508 Number of distinct products i*j*k with 1 <= i < j <= k <= n and j < n.

%I A083508 #16 Aug 04 2025 01:09:29
%S A083508 0,0,2,7,16,24,40,56,77,96,137,158,214,249,284,322,418,464,583,645,
%T A083508 708,774,946,1007,1125,1220,1330,1420,1685,1768,2069,2203,2346,2492,
%U A083508 2658,2750,3166,3362,3553,3675,4183,4344,4909,5129,5327,5575,6252,6432,6849
%N A083508 Number of distinct products i*j*k with 1 <= i < j <= k <= n and j < n.
%H A083508 Robert Israel, <a href="/A083508/b083508.txt">Table of n, a(n) for n = 1..1000</a>
%p A083508 V:= Vector(100):
%p A083508 S:= {}:
%p A083508 for n from 1 to 100 do
%p A083508   S:= S union {seq(i*(n-1)^2, i=1..n-2), seq(seq(i*j*n, i=1..j-1),j=2..n-1)};
%p A083508   V[n]:= nops(S);
%p A083508 od:
%p A083508 convert(V,list); # _Robert Israel_, Aug 03 2025
%o A083508 (PARI) for(n=1,100,s=Set();for(i=1,n-2,for(j=i+1,n-1,for(k=j,n,p=i*j*k;if(!setsearch(s,p),s=setunion(s,Set(p))))));print1(length(s),",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 06 2006
%Y A083508 Cf. A027430, A100435.
%K A083508 nonn
%O A083508 1,3
%A A083508 _N. J. A. Sloane_
%E A083508 Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 06 2006
%E A083508 Definition corrected by _Robert Israel_, Aug 03 2025