A181844 Sum over all partitions of n of the LCM of the parts.

1, 1, 3, 6, 12, 23, 38, 73, 118, 198, 318, 530, 819, 1298, 1974, 2975, 4516, 6698, 9980, 14550, 21186, 30304, 43503, 62030, 87908, 123292, 172543, 239720, 331688, 458198, 629376, 860332, 1168172, 1583176, 2138438, 2876283, 3859770, 5159886, 6863702, 9112356

Offset

0,3

Comments

Old name was: Row sums of A181842.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..188 (terms n=1..80 from Vincenzo Librandi)

Formula

a(n) = Sum_{k>=0} k * A256067(n,k) = Sum_{k>=0} A256553(n,k)*A256554(n,k). - Alois P. Heinz, Apr 02 2015

Maple

with(combstruct):
a181844 := proc(n) local k, L, l, R, part;
R := NULL; L := 0;
for k from 1 to n do
   part := iterstructs(Partition(n), size=k):
   while not finished(part) do
      l := nextstruct(part);
      L := L + ilcm(op(l));
   od;
od;
L end:
# second Maple program:
b:= proc(n, i, r) option remember; `if`(n=0, r, `if`(i<1, 0,
       b(n, i-1, r)+b(n-i, min(i, n-i), ilcm(i, r))))
    end:
a:= n-> b(n$2, 1):
seq(a(n), n=0..42);  # Alois P. Heinz, Mar 18 2019

Mathematica

t[n_, k_] := LCM @@@ IntegerPartitions[n, {n - k + 1}] // Total; a[n_] := Sum[t[n, k], {k, 1, n}]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Jul 26 2013 *)

Crossrefs

Cf. A078392 (the same for GCD), A181843, A181842, A256067, A256553, A256554, A306956.

Sequence in context: A249565 A174201 A327546 * A162506 A328609 A227681

Adjacent sequences: A181841 A181842 A181843 * A181845 A181846 A181847

Keyword

nonn

Author

Peter Luschny, Dec 07 2010

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 29 2015

New name from Alois P. Heinz, Mar 18 2019

Status

approved