A095849 Numbers j where sigma_k(j) increases to a record for all real values of k.

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

Offset: 1

Author

Matthew Vandermast, Jun 09 2004

Keywords

• nonn

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 k-th 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).

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