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Aaron Meyerowitz
Aaron Meyerowitz
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Not really an answer but too long for a comment.

The numbers start 1,232, 3, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 2310, 2310, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 30030, 30030, 60060, 60060

and the bold terms match (up to some leading 0's) largest LCM of a 5-partition of n. This sequence is not there exactly as is. However it is pretty close to largest lcm of partitions of n with a few hiccups. That is because the best partitions are the same most of the time and cosist of the first few primes with perhaps 4,8 or 9 included. Sometimes a prime near the end is skipped to get to the next prime. I imagine that after a partition like $[2,3,5,7,\cdots,89]$ things might get a bit more exciting since $91,93,95$ are all composite.

Not really an answer but too long for a comment.

The numbers start 1,23, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 2310, 2310, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 30030, 30030, 60060, 60060

and the bold terms match (up to some leading 0's) largest LCM of a 5-partition of n. This sequence is not there exactly as is. However it is pretty close to largest lcm of partitions of n with a few hiccups. That is because the best partitions are the same most of the time and cosist of the first few primes with perhaps 4,8 or 9 included. Sometimes a prime near the end is skipped to get to the next prime. I imagine that after a partition like $[2,3,5,7,\cdots,89]$ things might get a bit more exciting since $91,93,95$ are all composite.

Not really an answer but too long for a comment.

The numbers start 1,2, 3, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 2310, 2310, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 30030, 30030, 60060, 60060

and the bold terms match (up to some leading 0's) largest LCM of a 5-partition of n. This sequence is not there exactly as is. However it is pretty close to largest lcm of partitions of n with a few hiccups. That is because the best partitions are the same most of the time and cosist of the first few primes with perhaps 4,8 or 9 included. Sometimes a prime near the end is skipped to get to the next prime. I imagine that after a partition like $[2,3,5,7,\cdots,89]$ things might get a bit more exciting since $91,93,95$ are all composite.

Source Link
Aaron Meyerowitz
Aaron Meyerowitz
  • 30.1k
  • 1
  • 48
  • 104

Not really an answer but too long for a comment.

The numbers start 1,23, 6, 6, 12, 15, 30, 30, 60, 60, 84, 105, 210, 210, 420, 420, 420, 420, 840, 840, 1260, 1260, 2310, 2310, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 30030, 30030, 60060, 60060

and the bold terms match (up to some leading 0's) largest LCM of a 5-partition of n. This sequence is not there exactly as is. However it is pretty close to largest lcm of partitions of n with a few hiccups. That is because the best partitions are the same most of the time and cosist of the first few primes with perhaps 4,8 or 9 included. Sometimes a prime near the end is skipped to get to the next prime. I imagine that after a partition like $[2,3,5,7,\cdots,89]$ things might get a bit more exciting since $91,93,95$ are all composite.