A181849 -id:A181849 - cp's OEIS frontend

A181851 Triangle read by rows: T(n,k) = Sum_{c in composition(n,k)} lcm(c).

1, 2, 1, 3, 4, 1, 4, 8, 6, 1, 5, 20, 15, 8, 1, 6, 21, 50, 24, 10, 1, 7, 56, 66, 96, 35, 12, 1, 8, 60, 180, 160, 160, 48, 14, 1, 9, 96, 264, 432, 325, 244, 63, 16, 1, 10, 105, 510, 776, 892, 585, 350, 80, 18, 1, 11, 220, 567, 1704, 1835, 1668, 966, 480, 99, 20, 1

Offset: 1

Peter Luschny, Dec 07 2010

Composition(n,k) is the set of the k-tuples of positive integers which sum to n (see A181842). Taking the example in A181842, T(6,2) = lcm(5,1) + lcm(4,2) + lcm(3,3) + lcm(2,4) + lcm(1,5) = 5+4+3+4+5 = 21.

			[1]   1
[2]   2    1
[3]   3    4    1
[4]   4    8    6    1
[5]   5   20   15    8    1
[6]   6   21   50   24   10    1
[7]   7   56   66   96   35   12   1

Alois P. Heinz, Rows n = 1..150, flattened

Cf. A181849, A181850, A181853.

T(2n,n) gives A373865.

with(combstruct):
a181851_row := proc(n) local k,L,l,R,comp;
R := NULL;
for k from 1 to n do
   L := 0;
   comp := iterstructs(Composition(n),size=k):
   while not finished(comp) do
      l := nextstruct(comp);
      L := L + ilcm(op(l));
   od;
   R := R,L;
od;
R end:

c[n_, k_] := Permutations /@ IntegerPartitions[n, {k}] // Flatten[#, 1]&; t[n_, k_] := Total[LCM @@@ c[n, k]]; Table[t[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 05 2014 *)

A181850 Triangle read by rows: Partial row sums of A181851(n,k).

Original entry on oeis.org

1, 2, 3, 3, 7, 8, 4, 12, 18, 19, 5, 25, 40, 48, 49, 6, 27, 77, 101, 111, 112, 7, 63, 129, 225, 260, 272, 273, 8, 68, 248, 408, 568, 616, 630, 631, 9, 105, 369, 801, 1126, 1370, 1433, 1449, 1450, 10, 115, 625, 1401, 2293, 2878, 3228, 3308, 3326, 3327

Offset: 1

Peter Luschny, Dec 07 2010

			[1]   1
[2]   2    3
[3]   3    7     8
[4]   4   12    18    19
[5]   5   25    40    48    49
[6]   6   27    77   101   111   112
[7]   7   63   129   225   260   272   273

Alois P. Heinz, Rows n = 1..25, flattened

Cf. A181849, A181851, A181854.

with(combstruct):
a181850_row := proc(n) local k,L,l,R,comp;
R := NULL; L := 0;
for k from 1 to n do
   comp := iterstructs(Composition(n),size=k):
   while not finished(comp) do
      l := nextstruct(comp);
      L := L + ilcm(op(l));
   od;
   R := R,L;
od;
R end:

c[n_, k_] := Permutations /@ IntegerPartitions[n, {k}] // Flatten[#, 1]&; t[n_, k_] := Total[LCM @@@ c[n, k]]; Table[Print[row = Table[t[n, k], {k, 1, n}] // Accumulate]; row, {n, 1, 25}] // Flatten  (* Jean-François Alcover, Feb 05 2014 *)

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A181851 Triangle read by rows: T(n,k) = Sum_{c in composition(n,k)} lcm(c).

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