cp's OEIS Frontend

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

%I A181844 #31 Aug 14 2019 17:42:07
%S A181844 1,1,3,6,12,23,38,73,118,198,318,530,819,1298,1974,2975,4516,6698,
%T A181844 9980,14550,21186,30304,43503,62030,87908,123292,172543,239720,331688,
%U A181844 458198,629376,860332,1168172,1583176,2138438,2876283,3859770,5159886,6863702,9112356
%N A181844 Sum over all partitions of n of the LCM of the parts.
%C A181844 Old name was: Row sums of A181842.
%H A181844 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 A181844 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 A181844 with(combstruct):
%p A181844 a181844 := proc(n) local k,L,l,R,part;
%p A181844 R := NULL; L := 0;
%p A181844 for k from 1 to n do
%p A181844    part := iterstructs(Partition(n),size=k):
%p A181844    while not finished(part) do
%p A181844       l := nextstruct(part);
%p A181844       L := L + ilcm(op(l));
%p A181844    od;
%p A181844 od;
%p A181844 L end:
%p A181844 # second Maple program:
%p A181844 b:= proc(n, i, r) option remember; `if`(n=0, r, `if`(i<1, 0,
%p A181844        b(n, i-1, r)+b(n-i, min(i, n-i), ilcm(i, r))))
%p A181844     end:
%p A181844 a:= n-> b(n$2, 1):
%p A181844 seq(a(n), n=0..42);  # _Alois P. Heinz_, Mar 18 2019
%t A181844 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 A181844 Cf. A078392 (the same for GCD), A181843, A181842, A256067, A256553, A256554, A306956.
%K A181844 nonn
%O A181844 0,3
%A A181844 _Peter Luschny_, Dec 07 2010
%E A181844 a(0)=1 prepended by _Alois P. Heinz_, Mar 29 2015
%E A181844 New name from _Alois P. Heinz_, Mar 18 2019