A181844 - OEIS

%I #31 Aug 14 2019 17:42:07

%S 1,1,3,6,12,23,38,73,118,198,318,530,819,1298,1974,2975,4516,6698,

%T 9980,14550,21186,30304,43503,62030,87908,123292,172543,239720,331688,

%U 458198,629376,860332,1168172,1583176,2138438,2876283,3859770,5159886,6863702,9112356

%N Sum over all partitions of n of the LCM of the parts.

%C Old name was: Row sums of A181842.

%H Alois P. Heinz, <a href="/A181844/b181844.txt">Table of n, a(n) for n = 0..188</a> (terms n=1..80 from Vincenzo Librandi)

%F a(n) = Sum_{k>=0} k * A256067(n,k) = Sum_{k>=0} A256553(n,k)*A256554(n,k). - _Alois P. Heinz_, Apr 02 2015

%p with(combstruct):

%p a181844 := proc(n) local k,L,l,R,part;

%p R := NULL; L := 0;

%p for k from 1 to n do

%p    part := iterstructs(Partition(n),size=k):

%p    while not finished(part) do

%p       l := nextstruct(part);

%p       L := L + ilcm(op(l));

%p    od;

%p od;

%p L end:

%p # second Maple program:

%p b:= proc(n, i, r) option remember; `if`(n=0, r, `if`(i<1, 0,

%p        b(n, i-1, r)+b(n-i, min(i, n-i), ilcm(i, r))))

%p     end:

%p a:= n-> b(n$2, 1):

%p seq(a(n), n=0..42);  # _Alois P. Heinz_, Mar 18 2019

%t 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 *)

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

%K nonn

%O 0,3

%A _Peter Luschny_, Dec 07 2010

%E a(0)=1 prepended by _Alois P. Heinz_, Mar 29 2015

%E New name from _Alois P. Heinz_, Mar 18 2019