A261342 Numbers n such that either floor(n^(1/k)) or ceiling(n^(1/k)) divides n for all integers k >= 1.

1, 2, 3, 4, 6, 8, 9, 12, 15, 16, 20, 24, 30, 36, 42, 48, 56, 63, 64, 72, 80, 90, 100, 120, 132, 144, 156, 168, 195, 210, 224, 240, 288, 324, 360, 400, 420, 440, 528, 552, 576, 600, 624, 675, 702, 756, 840, 870, 900, 930, 960, 1056, 1155, 1260, 1332, 1368, 1560, 1680, 1764, 1848, 1980, 2352, 2600, 2704

Offset: 1

Author

Max Alekseyev, Aug 15 2015

Keywords

• nonn

Comments

Largest known term is a(278) = 8947091986560.

If it exists, a(279) > 10^16.

Is this sequence finite?

Links

• Max Alekseyev, Table of n, a(n) for n = 1..278

Crossrefs

Contains A261205, A261206, A261341 as subsequences.

Subsequence of A006446.

Programs

PARI

{ isA261342(n) = my(k,t1,t2); k=2; until(t2<=2, t1=floor(sqrtn(n+.5,k)); t2=ceil(sqrtn(n-.5,k)); if(n%t1 && n%t2, return(0)); k++); 1; }