32 lines
722 B
Text
32 lines
722 B
Text
ClearAll[PowerfulNumberQ, StrongAchillesNumberQ]
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PowerfulNumberQ[n_Integer] := AllTrue[FactorInteger[n][[All, 2]], GreaterEqualThan[2]]
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AchillesNumberQ[n_Integer] := Module[{divs},
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If[PowerfulNumberQ[n],
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divs = Divisors[n];
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If[Length[divs] > 2,
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divs = divs[[2 ;; -2]];
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!AnyTrue[Log[#, n] & /@ divs, IntegerQ]
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,
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True
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]
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,
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False
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]
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]
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StrongAchillesNumberQ[n_] := AchillesNumberQ[n] \[And] AchillesNumberQ[EulerPhi[n]]
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n = 0;
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i = 0;
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Reap[While[n < 50,
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i++;
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If[AchillesNumberQ[i], n++; Sow[i]]
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]][[2, 1]]
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n = 0;
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i = 0;
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Reap[While[n < 20,
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i++;
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If[StrongAchillesNumberQ[i], n++; Sow[i]]
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]][[2, 1]]
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Tally[IntegerLength /@ Select[Range[9999999], AchillesNumberQ]] // Grid
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