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.
%I A359195 #9 Jan 06 2023 20:47:11 %S A359195 1,4,16,32,36,72,144,288,432,864,1728,3456,3600,5400,7200,10800,21600, %T A359195 43200,86400,151200,172800,216000,302400 %N A359195 Positive integers k with a smaller fraction of powers (mod k) than any smaller positive integers. %C A359195 It seems that a(n) <= 2*a(n-1) for n > 3. %C A359195 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, .... %e A359195 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. %e A359195 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. %Y A359195 A085635 is the analogous sequence for squares. %Y A359195 Cf. A025487, A337868. %K A359195 nonn,more %O A359195 1,2 %A A359195 _Charles R Greathouse IV_, Dec 19 2022