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A208767
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Generalized 2-super abundant numbers.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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S. Sivasankaranarayana Pillai, Highly abundant numbers, Bulletin of the Calcutta Mathematical Society, Vol. 35, No. 1 (1943), pp. 141-156.
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FORMULA
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EXAMPLE
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For i=24, sigma_2(24)/(24^2)=850/576=1.47569, a new record, thus 24 is in the sequence.
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MATHEMATICA
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s = {1}; a = 1; Do[ If[DivisorSigma[2, n]/(n^2) > a, a = DivisorSigma[2, n]/(n^2); AppendTo[s, n]], {n, 10000000}]; s
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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