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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 Table of n, a(n) for n=1..91. 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 Adjacent sequences: A181843 A181844 A181845 * A181847 A181848 A181849 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.)