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%I #21 Jan 15 2021 21:33:13
%S 1,15,90,310,990,2220,5300,9660,17130,28670,52848,75696,128541,183393,
%T 257628,344316,529038,683316,1001110,1256010,1607004,2049490,2837700,
%U 3330636,4177186,5150340,6273810,7432702,9779991,11124711,14381168,16610640,19542393,23032799,26873769
%N Sum of distinct products i*j*k with 1 <= i, j, k <= n.
%H Michael S. Branicky, <a href="/A323334/b323334.txt">Table of n, a(n) for n = 1..2302</a> (terms 1..500 from Seiichi Manyama)
%e a(2) = 1 + 2 + 4 + 8 = 15.
%e a(3) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 27 = 90.
%t a[n_] := Table[i j k, {i, n}, {j, n}, {k, n}] // Flatten // Union // Total;
%t Array[a, 35] (* _Jean-François Alcover_, Nov 25 2020 *)
%o (Python)
%o def aupton(terms):
%o alst, s, pset = [], 0, set()
%o for n in range(1, terms):
%o for i in range(1, n+1):
%o for j in range(i, n+1):
%o p = i*j*n # k = n
%o if p not in pset:
%o pset.add(p)
%o s += p
%o alst.append(s)
%o return alst
%o print(aupton(36)) # _Michael S. Branicky_, Jan 15 2021
%Y Column 3 of A321163.
%Y Cf. A027425.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jan 11 2019
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