cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A122978 Number of sublattices of the division lattice of divisors of n.

Original entry on oeis.org

1, 3, 3, 7, 3, 12, 3, 15, 7, 12, 3, 37, 3, 12, 12, 31, 3, 37, 3, 37, 12, 12, 3, 103, 7, 12, 15, 37, 3, 73, 3, 63, 12, 12, 12, 146, 3, 12, 12, 103, 3, 73, 3, 37, 37, 12, 3, 271, 7, 37, 12, 37, 3, 103, 12, 103, 12, 12, 3, 319, 3, 12, 37, 127, 12, 73, 3, 37, 12, 73, 3, 505, 3, 12, 37, 37
Offset: 1

Views

Author

Franklin T. Adams-Watters, Sep 21 2006

Keywords

Comments

A division lattice is closed under GCD and LCM. Depends only on the prime signature of n.

Crossrefs

Cf. A051839, A122977, A122981, A122982.

A122979 Number of distributive sublattices of the lattice of k-tuples less than the n-th partition (in Abramowitz and Stegun order), that include the maximum element.

Original entry on oeis.org

2, 4, 7, 8, 21, 45, 16, 58, 84, 200, 500, 32, 152, 293, 748, 1184, 3220
Offset: 1

Views

Author

Franklin T. Adams-Watters, Sep 21 2006

Keywords

Comments

After a(18) - for partition [1^5] - the sequence continues ?, 64, 384, 938, 1238, 2520, 5591, ?, ?, ?, ?, ?, 128.

Examples

			For a(5), partition [2,1], the lattice consists of the 6 pairs (i,j) where 0<=i<=2 and 0<=j<=1, with (i,j) <= (i',j') iff i<=i' and j<=j'. {(2,1), (2,0), (0,1), (0,0)} is one distributive sublattice.

Links

  • M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A122977, A122980, A122981, A036036, A074139.

A122982 Number of distributive sublattices of the lattice of k-tuples less than the n-th partition (in Mathematica order).

Original entry on oeis.org

3, 7, 12, 15, 37, 73, 31, 103, 146, 319, 731, 63, 271, 505, 1191, 1833, 4618
Offset: 1

Views

Author

Franklin T. Adams-Watters, Sep 21 2006

Keywords

Comments

After a(18) - for partition [1^5] - the sequence continues ?, 127, 687, 1611, 4031, 2102, 8589, ?, ?, ?, ?, ?, 255.

Examples

			For a(5), partition [2,1], the lattice consists of the 6 pairs (i,j) where 0<=i<=2 and 0<=j<=1, with (i,j) <= (i',j') iff i<=i' and j<=j'. {(2,1), (2,0), (0,1), (0,0)} is one distributive sublattice.

Crossrefs

Cf. A122978, A122981, A122980, A080577, A074139.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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