

A208767


Generalized 2super abundant numbers.


1



1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 720, 840, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 360360, 720720, 1441440, 2162160, 3603600, 4324320, 7207200
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OFFSET

1,2


COMMENTS

The generalized ksuper abundant numbers are those such that sigma_k(n)/(n^k) > sigma_k(m)/(m^k) for all m < n, where sigma_k(n) is the sum of the kth powers of the divisors of n.
1super abundant numbers are A004394. 0super abundant numbers are A002182.


LINKS

Table of n, a(n) for n=1..32.


EXAMPLE

For i=24, sigma_2(24)/(24^2)=850/576=1.47569, a new record, thus 24 is in the sequence.


MATHEMATICA

s = {1}; a = 1; Do[ If[DivisorSigma[2, n]/(n^2) > a, a = DivisorSigma[2, n]/(n^2); AppendTo[s, n]], {n, 10000000}]; s


CROSSREFS

Cf. A002182, A004394, A004490, A002201, A001157.
Sequence in context: A047151 A068010 A095848 * A136339 A019505 A135614
Adjacent sequences: A208764 A208765 A208766 * A208768 A208769 A208770


KEYWORD

nonn


AUTHOR

Ben Branman, Mar 01 2012


STATUS

approved



