A091717 Triangular array read by rows: Greatest common divisors of values of the partition function P: T(n,k) = gcd(P(n), P(k)), 0 <= k < n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 2, 1, 1, 1, 11, 1, 1, 1, 2, 3, 5, 1, 1, 15, 2, 1, 1, 2, 3, 1, 7, 1, 3, 2, 6, 1, 1, 2, 1, 1, 7, 1, 1, 2, 2, 14, 1, 1, 1, 1, 1, 7, 11, 1, 11, 1, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 15, 1

Offset

1,25

Links

Amiram Eldar, Table of n, a(n) for n = 1..11175, rows 1..150 in flattened form.

Formula

A091718(n) = Max_{k=0..n-1} T(n,k);

T(n,0) = T(n,1) = 1; T(n,n-1) = A091719(n-1).

Example

Triangle begins:
1
1, 1
1, 1, 1
1, 1, 1, 1
1, 1, 1, 1, 1
1, 1, 1, 1, 1, 1
1, 1, 1, 3, 5, 1, 1
1, 1, 2, 1, 1, 1, 11, 1
...

Mathematica

m = 15; p = PartitionsP[Range[0, m]]; Table[GCD[p[[i]], p[[j]]], {i, 1, m}, {j, 1, i - 1}] // Flatten (* Amiram Eldar, May 10 2020 *)

Crossrefs

Cf. A000041, A091718, A091719.

Sequence in context: A011353 A016452 A346095 * A355815 A154512 A030588

Adjacent sequences: A091714 A091715 A091716 * A091718 A091719 A091720

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Feb 01 2004

Status

approved