

A095849


Numbers j where sigma_k(j) increases to a record for all real values of k.


4



1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 840, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 720720, 1441440, 2162160, 3603600, 7207200, 10810800, 36756720, 61261200, 122522400, 183783600, 698377680
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OFFSET

1,2


COMMENTS

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 kth powers of all divisors of j.
Conjecture: a number is in this sequence if and only if it is in both A002182 and A095848.  J. Lowell, Jun 21 2008


LINKS

T. D. Noe, Table of n, a(n) for n = 1..74 (complete) [I assume this is only conjectured to be complete.  N. J. A. Sloane, Jan 02 2019]


CROSSREFS

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.
Cf. also A166981 (numbers that establish records for both k=0 and k=1).
Sequence in context: A350049 A135614 A115387 * A094783 A058764 A087009
Adjacent sequences: A095846 A095847 A095848 * A095850 A095851 A095852


KEYWORD

nonn


AUTHOR

Matthew Vandermast, Jun 09 2004


EXTENSIONS

Extended by T. D. Noe, Apr 22 2010
Corrected by T. D. Noe and Matthew Vandermast, Oct 04 2010
Removed keyword "fini", since it appears that as yet there is no proof.  N. J. A. Sloane, Sep 17 2022


STATUS

approved



