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