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%I #42 Sep 20 2022 14:23:58
%S 1,2,4,6,12,24,48,60,120,240,360,840,1680,2520,5040,10080,15120,25200,
%T 27720,55440,110880,166320,277200,720720,1441440,2162160,3603600,
%U 7207200,10810800,36756720,61261200,122522400,183783600,698377680
%N Numbers j where sigma_k(j) increases to a record for all real values of k.
%C For any value of k, sigma_k(j) > sigma_k(m) for all m < j, where the function sigma_k(j) is the sum of the k-th powers of all divisors of j.
%C Conjecture: a number is in this sequence if and only if it is in both A002182 and A095848. - _J. Lowell_, Jun 21 2008
%H T. D. Noe, <a href="/A095849/b095849.txt">Table of n, a(n) for n = 1..74</a> (complete) [I assume this is only conjectured to be complete. - _N. J. A. Sloane_, Jan 02 2019]
%Y Cf. A002093 (highly abundant numbers), A002182 (highly composite numbers) and A004394 (superabundant numbers), consisting of numbers that establish records for sigma_k(j) where k equals 1, 0 and -1 respectively. See also A095848.
%Y Cf. also A166981 (numbers that establish records for both k=0 and k=-1).
%K nonn
%O 1,2
%A _Matthew Vandermast_, Jun 09 2004
%E Extended by _T. D. Noe_, Apr 22 2010
%E Corrected by _T. D. Noe_ and _Matthew Vandermast_, Oct 04 2010
%E Removed keyword "fini", since it appears that as yet there is no proof. - _N. J. A. Sloane_, Sep 17 2022
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