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Search: id:A093771
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| A093771 |
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Perfect powers for which the exponent is a prime number: solutions to {A051409(x) is prime}. |
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+0
1
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| 4, 8, 9, 25, 27, 32, 36, 49, 100, 121, 125, 128, 144, 169, 196, 216, 225, 243, 289, 324, 343, 361, 400, 441, 484, 529, 576, 676, 784, 841, 900, 961, 1000, 1089, 1156, 1225, 1331, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936, 2025, 2048, 2116, 2187
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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GCD of prime-exponents in canonical factorization of n is prime.
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EXAMPLE
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All 2-,3-,5-,7th ... powers are here, 4-,6-,8th etc. powers are excluded
from A001597.
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MATHEMATICA
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ffi[x_] :=Flatten[FactorInteger[x]] ep[x_] :=Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] lf[x_] :=Length[FactorInteger[x]] Do[If[PrimeQ[Apply[GCD, ep[n]]], Print[n]], {n, 2, 10000}]
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CROSSREFS
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Cf. A001157, A025479, A052409.
Sequence in context: A035326 A063907 A056166 this_sequence A051676 A114129 A053810
Adjacent sequences: A093768 A093769 A093770 this_sequence A093772 A093773 A093774
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 19 2004
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