

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



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).


KEYWORD

nonn


AUTHOR



EXTENSIONS

Removed keyword "fini", since it appears that as yet there is no proof.  N. J. A. Sloane, Sep 17 2022


STATUS

approved



