A323334 Sum of distinct products i*j*k with 1 <= i, j, k <= n.

1, 15, 90, 310, 990, 2220, 5300, 9660, 17130, 28670, 52848, 75696, 128541, 183393, 257628, 344316, 529038, 683316, 1001110, 1256010, 1607004, 2049490, 2837700, 3330636, 4177186, 5150340, 6273810, 7432702, 9779991, 11124711, 14381168, 16610640, 19542393, 23032799, 26873769

Offset: 1

Author

Seiichi Manyama, Jan 11 2019

Keywords

• nonn

Examples

			a(2) = 1 + 2 + 4 + 8 = 15.
a(3) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 27 = 90.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..2302 (terms 1..500 from Seiichi Manyama)

Crossrefs

Column 3 of A321163.

Cf. A027425.

Programs

Mathematica

a[n_] := Table[i j k, {i, n}, {j, n}, {k, n}] // Flatten // Union // Total;
Array[a, 35] (* Jean-François Alcover, Nov 25 2020 *)

Python

def aupton(terms):
  alst, s, pset = [], 0, set()
  for n in range(1, terms):
    for i in range(1, n+1):
      for j in range(i, n+1):
        p = i*j*n # k = n
        if p not in pset:
          pset.add(p)
          s += p
    alst.append(s)
  return alst
print(aupton(36)) # Michael S. Branicky, Jan 15 2021