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A319054
Maximum product of an aperiodic integer partition of n.
1
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.
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 09 2018
STATUS
approved