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A328014
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Numbers whose powerful part (A057521) is larger than their powerfree part (A055231).
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4
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4, 8, 9, 12, 16, 18, 24, 25, 27, 32, 36, 40, 45, 48, 49, 50, 54, 56, 63, 64, 72, 75, 80, 81, 96, 98, 100, 108, 112, 121, 125, 128, 135, 144, 147, 150, 160, 162, 169, 175, 176, 180, 189, 192, 196, 200, 208, 216, 224, 225, 240, 242, 243, 245, 250, 252, 256, 270
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OFFSET
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1,1
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COMMENTS
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Differs from A122145(n) at n >= 25.
Cloutier et al. showed that the number of terms of this sequence below x is D0 * x^(3/4) + O(x^(2/3)*log(x)), where D0 is a constant given in A328015.
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LINKS
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EXAMPLE
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MATHEMATICA
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funp[p_, e_] := If[e > 1, p^e, 1]; pow[n_] := Times @@ (funp @@@ FactorInteger[n]); aQ[n_] := pow[n] > n/pow[n]; Select[Range[1000], aQ]
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PROG
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(PARI) pful(f) = prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); \\ A057521
pfree(f) = for (k=1, #f~, if (f[k, 2] > 1, f[k, 2] = 0); ); factorback(f); \\ A055231
isok(n) = my(f=factor(n)); pful(f) > pfree(f); \\ Michel Marcus, Oct 02 2019
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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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