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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Charles R Greathouse IV, Dec 19 2022

Keywords

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.
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