A359195 Positive integers k with a smaller fraction of powers (mod k) than any smaller positive integers.

1, 4, 16, 32, 36, 72, 144, 288, 432, 864, 1728, 3456, 3600, 5400, 7200, 10800, 21600, 43200, 86400, 151200, 172800, 216000, 302400

Offset: 1

Author

Charles R Greathouse IV, Dec 19 2022

Keywords

• nonn
• more

Comments

It seems that a(n) <= 2*a(n-1) for n > 3.

Conjecture: terms are products of primorials (A025487). A proof would greatly speed the search for more terms. On this conjecture, the next terms are 352800, 529200, 1058400, 2116800, 4233600, 6350400, 10584000, 19051200, 21168000, 31752000, 63504000, ....

Examples

			2 is not a square or a cube mod 4, while 0, 1, and 3 are all cubes mod 4. 1/4 is a record, so 4 is in the sequence.
None of 2, 4, 6, 10, 12, 14 are cubes mod 16 and of those only 4 is a square and none are 5th powers, for a 5/16 fraction, which is a record, so 16 is in the sequence.
		

Crossrefs

A085635 is the analogous sequence for squares.

Cf. A025487, A337868.