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A181844 Sum over all partitions of n of the LCM of the parts. 9
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 (list; graph; refs; listen; history; text; internal format)
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
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

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Last modified April 23 07:57 EDT 2024. Contains 371905 sequences. (Running on oeis4.)