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A077006
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Numbers k such that sigma(k)/k >= sigma(m)/m for all m <= k.
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3
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1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 360360, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800, 21621600
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OFFSET
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1,2
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COMMENTS
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A004394 is a subsequence. I searched to 2^150 for terms that are not in A004394 and found only a(29)=360360. Are there more near-miss superabundant numbers like 360360? - Jeppe Stig Nielsen, Dec 23 2022
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LINKS
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EXAMPLE
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360360 is included in this sequence (but not in A004394) because its abundancy (sigma(k)/k = 48/11) is the same as that of the previous record holder (namely 332640). - Gerard P. Michon, May 20 2009
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MATHEMATICA
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abund[n_] := abund[n] = DivisorSigma[1, n]/n; ok[n_] := (r = True; m = 1; While[m <= n, If[abund[n] < abund[m], r = False; Break[]]; m++]; r); n = 1; A077006 = {}; While[n < 10^6, If[ok[n], Print[n]; AppendTo[ A077006, n]]; n++]; A077006 (* Jean-François Alcover, Dec 12 2011 *)
DeleteDuplicates[Table[{n, DivisorSigma[1, n]/n}, {n, 2163*10^4}], Greater[ #1[[2]], #2[[2]]]&] [[All, 1]] (* Harvey P. Dale, Sep 02 2022 *)
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CROSSREFS
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KEYWORD
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nice,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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