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A052486
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Achilles numbers - powerful but imperfect: writing n=product(p_i^e_i) then none of the e_i=1 (i.e. powerful(1)) but the highest common factor of the e_i>1 is 1 (so not perfect powers).
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11
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72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1800, 1944, 2000, 2312, 2592, 2700, 2888, 3087, 3200, 3267, 3456, 3528, 3872, 3888, 4000, 4232, 4500, 4563, 4608, 5000, 5292, 5324, 5400, 5408, 5488
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OFFSET
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1,1
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Achilles Number
Project Euler, Problem 302. [From M. F. Hasler, Sep 23 2010]
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EXAMPLE
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a(3)=200 because 200=2^3*5^2, both 3 and 2 are greater than 1, and the highest common factor of 3 and 2 is 1.
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MATHEMATICA
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achillesQ[n_] := Block[{ls = Last /@ FactorInteger@n}, Min@ ls > 1 == GCD @@ ls]; Select[ Range@ 5500, achillesQ@# &] (* From Robert G. Wilson v, Jun 10 2010 *)
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PROG
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(PARI) isA052486(n) = { n>1 & vecmin(factor(n)[, 2])>1 & !ispower(n) } \\ From M. F. Hasler, Sep 23 2010
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CROSSREFS
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Cf. A001597, A001694, A007916.
Sequence in context: A102562 A216426 A072412 * A114128 A143610 A166987
Adjacent sequences: A052483 A052484 A052485 * A052487 A052488 A052489
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley, Mar 16 2000
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EXTENSIONS
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Example edited by Mac Coombe (mac.coombe(AT)gmail.com), Sep 18 2010
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STATUS
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approved
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