A181850 -id:A181850 - 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 *)

A181849 Row sums of A181851.

Original entry on oeis.org

1, 1, 3, 8, 19, 49, 112, 273, 631, 1450, 3327, 7571, 17170, 38519, 85951, 190392, 419759, 921189, 2013874, 4385889, 9516273, 20577618, 44352499, 95324853, 204307052, 436768151, 931448065, 1981879262, 4207887155, 8916102661, 18856430826, 39807226901, 83892649091

Offset: 0

Peter Luschny, Dec 07 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..150

Cf. A181850, A181851.

with(combstruct):
a181849 := proc(n) local k,L,l,comp;
L := 1-signum(n);
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;
od;
L end:
seq(a181849(n), n=0..15);

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

a(23)-a(25) from Alois P. Heinz, Jul 29 2013

a(0), a(26)-a(32) from Alois P. Heinz, Jun 18 2024

cp's OEIS Frontend

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

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