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A189045
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Semiprimes which are sub-perfect powers.
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3
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15, 26, 35, 143, 215, 323, 511, 899, 1727, 1763, 2047, 2186, 2743, 3599, 5183, 7999, 10403, 11663, 13823, 19043, 22499, 32399, 36863, 39203, 51983, 54871, 57599, 72899, 79523, 97343, 121103, 157463, 176399, 186623, 213443, 238327, 248831, 272483, 279935, 324899, 359999, 381923
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OFFSET
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1,1
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COMMENTS
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Numbers of the form p*q where p and q are primes, not necessarily distinct, such that p*q + 1 is a perfect power (squares, cubes, etc.). In one sense, this is to semiprimes as Mersenne primes A000668 are to primes.
By Catalan's conjecture (or now Mihailescu's theorem), p and q are always distinct. - T. D. Noe, Apr 15 2011
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LINKS
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FORMULA
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EXAMPLE
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a(9) = 12^3 - 1 = 1727 = 11 * 157.
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MATHEMATICA
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SemiPrimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; PerfectPowerQ[n_] := GCD @@ Last /@ FactorInteger[n] > 1; Select[Range[400000], SemiPrimeQ[#] && PerfectPowerQ[# + 1] &] (* T. D. Noe, Apr 15 2011 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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