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

1,2

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, ....

Links

Table of n, a(n) for n=1..23.

Example

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.

Sequence in context: A324784 A046001 A239611 * A373077 A031050 A243980

Adjacent sequences: A359192 A359193 A359194 * A359196 A359197 A359198

Keyword

nonn,more

Author

Charles R Greathouse IV, Dec 19 2022

Status

approved