A319054 Maximum product of an aperiodic integer partition of n.

1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 54, 72, 108, 162, 216, 324, 486, 648, 972, 1458, 1944, 2916, 4374, 5832, 8748, 13122, 17496, 26244, 39366, 52488, 78732, 118098, 157464, 236196, 354294, 472392, 708588, 1062882, 1417176, 2125764, 3188646, 4251528, 6377292

Offset

1,2

Comments

An integer partition is aperiodic if its multiplicities are relatively prime.

Links

Table of n, a(n) for n=1..43.

Example

Among the aperiodic partitions of 9, those with maximum product are (432) and (3222), so a(9) = 24. If periodic partitions were allowed, we would have (333) with product 27.

Mathematica

Table[Max[Times@@@Select[IntegerPartitions[n], GCD@@Length/@Split[#]==1&]], {n, 30}]

Crossrefs

Cf. A000740, A000792, A000793, A000837, A007916, A100953, A281116, A289508, A289509, A296302.

Sequence in context: A001461 A048597 A332839 * A074964 A017822 A292772

Adjacent sequences: A319051 A319052 A319053 * A319055 A319056 A319057

Keyword

nonn

Author

Gus Wiseman, Sep 09 2018

Status

approved