cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A321165 Sum of distinct products i*j with 1 <= i, j <= n.

Original entry on oeis.org

1, 7, 25, 61, 136, 244, 440, 680, 1022, 1472, 2198, 2882, 4065, 5241, 6681, 8265, 10866, 13116, 16726, 19786, 23566, 27922, 34270, 38902, 45502, 52600, 60430, 68326, 80941, 89671, 105047, 116855, 130913, 146519, 163214, 177002, 203013, 224673, 247605, 268005, 303306
Offset: 1

Views

Author

Seiichi Manyama, Jan 10 2019

Keywords

Examples

			a(2) = 1 + 2 + 4 = 7.
a(3) = 1 + 2 + 3 + 4 + 6 + 9 = 25.

Links

Crossrefs

Column 2 of A321163.
Cf. A027424.

Programs

  • PARI
    a(n) = vecsum(setbinop((x, y)->x*y, vector(n, i, i); )); \\ Michel Marcus, Jan 10 2019

Formula

a(p) = a(p - 1) + p ^ 2 * (p + 1) / 2 for prime p. - David A. Corneth, Jan 10 2019

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Jan 11 2019

Keywords

Examples

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

Links

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

A321164 Sum of distinct products b_1*b_2*...*b_n where 1<=b_i<=n.

Original entry on oeis.org

1, 7, 90, 1441, 38325, 916714, 37830100, 1194352181, 45241845825, 1951734678972, 147430334155104, 5664495439368403, 528359397843879784, 30798685780200874044, 1774211038440007650672, 99969666291681633988821, 13249072759407029981640765, 847264606120975715873578180
Offset: 1

Views

Author

Seiichi Manyama, Jan 10 2019

Keywords

Examples

			a(2) = 1 + 2 + 4 = 7.
a(3) = 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 27 = 90.

Crossrefs

Main diagonal of A321163.
Cf. A110713.

Programs

  • Maple
    a:= proc(m) option remember; local b; b:=
      proc(n) option remember; `if`(n=0, {1},
        map(x-> seq(x*i, i=1..m), b(n-1)))
      end; forget(b); add(i, i=b(m))
    end:
seq(a(n), n=1..12);  # Alois P. Heinz, Jan 11 2019
  • Mathematica
    a[m_] := a[m] = Module[{b}, b[n_] := b[n] = If[n==0, {1}, Map[Table[# i, {i, 1, m}]&, b[n-1]]] // Flatten // Union; b[m] // Total];
Array[a, 12] (* Jean-François Alcover, Nov 26 2020, after Alois P. Heinz *)

Extensions

a(15)-a(18) from Alois P. Heinz, Jan 11 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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