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A353538
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Numbers k such that k and k+1 both have an abundancy index that is larger than Pi^2/6.
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6
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44, 63, 75, 104, 135, 164, 188, 189, 195, 224, 230, 231, 255, 284, 285, 315, 344, 374, 375, 404, 405, 434, 435, 440, 441, 464, 494, 495, 524, 567, 584, 675, 692, 735, 764, 819, 824, 825, 854, 855, 944, 945, 975, 1034, 1035, 1070, 1071, 1124, 1155, 1196, 1215, 1274
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OFFSET
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1,1
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COMMENTS
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The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 3, 43, 399, 4292, 41306, 413310, 4155925, 414963651, 4149603572, ...
Apparently, the asymptotic density of this sequence is 0.04149...
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LINKS
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EXAMPLE
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44 is a term since sigma(44)/44 = 84/44 = 1.909... and sigma(45)/45 = 78/45 = 1.733... are both larger than Pi^2/6 = 1.644... .
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MATHEMATICA
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q[n_] := DivisorSigma[-1, n] > Pi^2/6; Select[Range[1300], q[#] && q[# + 1] &]
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PROG
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(PARI) isok(k) = ((sigma(k)/k) > Pi^2/6) && ((sigma(k+1)/(k+1)) > Pi^2/6); \\ Michel Marcus, Apr 25 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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