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A208767 Generalized 2-super abundant numbers. 2
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, 10810800, 12252240, 21621600, 24504480, 36756720, 61261200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The generalized k-super 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 k-th powers of the divisors of n.

1-super abundant numbers are A004394. 0-super abundant numbers are A002182.

Pillai called these numbers "highly abundant numbers of the 2nd order". - Amiram Eldar, Jun 30 2019

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..251

S. Sivasankaranarayana Pillai, Highly abundant numbers, Bulletin of the Calcutta Mathematical Society, Vol. 35,  No. 1 (1943), pp. 141-156.

S. Sivasankaranarayana Pillai, On numbers analogous to highly composite numbers of Ramanujan, Rajah Sir Annamalai Chettiar Commemoration Volume, ed. Dr. B. V. Narayanaswamy Naidu, Annamalai University, 1941, pp. 697-704.

Srinivasa Ramanujan, Highly composite numbers, Annotated and with a foreword by Jean-Louis Nicolas and Guy Robin, The Ramanujan Journal, Vol. 1, No. 2 (1997), pp. 119-153, alternative link.

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.

Subsequence of A025487.

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

EXTENSIONS

More terms from Amiram Eldar, May 12 2019

STATUS

approved

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)