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A357685
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Numbers k such that A293228(k) > k.
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3
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30, 42, 60, 66, 70, 78, 84, 102, 114, 132, 138, 140, 156, 174, 186, 204, 210, 222, 228, 246, 258, 276, 282, 318, 330, 348, 354, 366, 372, 390, 402, 420, 426, 438, 444, 462, 474, 492, 498, 510, 516, 534, 546, 564, 570, 582, 606, 618, 636, 642, 654, 660, 678, 690
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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 7, 79, 843, 8230, 83005, 826875, 8275895, 82790525, 827718858, 8276571394, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0827... .
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LINKS
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EXAMPLE
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30 is a term since its aliquot squarefree divisors are {1, 2, 3, 5, 6, 10, 15} and their sum is 42 > 30.
60 is a term since its aliquot squarefree divisors are {1, 2, 3, 5, 6, 10, 15, 30} and their sum is 72 > 60.
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MATHEMATICA
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s[n_] := Times @@ (1 + (f = FactorInteger[n])[[;; , 1]]) - If[AllTrue[f[[;; , 2]], # == 1 &], n, 0]; Select[Range[2, 1000], s[#] > # &]
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PROG
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(PARI) is(n) = {my(f = factor(n), s); s = prod(i=1, #f~, f[i, 1]+1); if(n==1 || vecmax(f[, 2]) == 1, s -= n); s > n};
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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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