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A181846 Triangle read by rows: T(n,k) = Sum_{c in P(n,n-k+1)} gcd(c) where P(n,m) = A008284(n,m) is the number of partitions of n into m parts. 0
1, 1, 2, 1, 1, 3, 1, 1, 3, 4, 1, 1, 2, 2, 5, 1, 1, 2, 4, 6, 6, 1, 1, 2, 3, 4, 3, 7, 1, 1, 2, 3, 6, 6, 8, 8, 1, 1, 2, 3, 5, 6, 9, 6, 9, 1, 1, 2, 3, 5, 8, 10, 10, 11, 10, 1, 1, 2, 3, 5, 7, 10, 11, 10, 5, 11, 1, 1, 2, 3, 5, 7, 12, 14, 19, 19, 17, 12, 1, 1, 2, 3, 5, 7, 11, 14, 18, 18, 14, 6, 13 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
See A181842 for the definition of 'partition'.
LINKS
EXAMPLE
[1] 1
[2] 1 2
[3] 1 1 3
[4] 1 1 3 4
[5] 1 1 2 2 5
[6] 1 1 2 4 6 6
[7] 1 1 2 3 4 3 7
MAPLE
with(combstruct):
a181846_row := proc(n) local k, L, l, R, part;
R := NULL;
for k from 1 to n do
L := 0;
part := iterstructs(Partition(n), size=n-k+1):
while not finished(part) do
l := nextstruct(part);
L := L + igcd(op(l));
od;
R := R, L;
od;
R end:
MATHEMATICA
T[n_, k_] := GCD @@@ IntegerPartitions[n, {n-k+1}] // Total;
Table[T[n, k], {n, 1, 13}, {k, 1, n}] (* Jean-François Alcover, Jun 22 2019 *)
CROSSREFS
Cf. A078392.
Sequence in context: A300649 A086599 A353947 * A305499 A210873 A224838
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Dec 07 2010
EXTENSIONS
Extended to 13 rows by Jean-François Alcover, Jun 22 2019
STATUS
approved

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Last modified February 27 19:24 EST 2024. Contains 370378 sequences. (Running on oeis4.)