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%I #11 Aug 09 2017 23:10:02
%S 1,2,3,4,6,8,9,12,15,16,20,24,30,36,42,48,56,63,64,72,80,90,100,120,
%T 132,144,156,168,195,210,224,240,288,324,360,400,420,440,528,552,576,
%U 600,624,675,702,756,840,870,900,930,960,1056,1155,1260,1332,1368,1560,1680,1764,1848,1980,2352,2600,2704
%N Numbers n such that either floor(n^(1/k)) or ceiling(n^(1/k)) divides n for all integers k >= 1.
%C Largest known term is a(278) = 8947091986560.
%C If it exists, a(279) > 10^16.
%C Is this sequence finite?
%H Max Alekseyev, <a href="/A261342/b261342.txt">Table of n, a(n) for n = 1..278</a>
%o (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; }
%Y Contains A261205, A261206, A261341 as subsequences.
%Y Subsequence of A006446.
%K nonn,more
%O 1,2
%A _Max Alekseyev_, Aug 15 2015