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A052486 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). 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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]

EXAMPLE

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.

MATHEMATICA

achillesQ[n_] := Block[{ls = Last /@ FactorInteger@n}, Min@ ls > 1 == GCD @@ ls]; Select[ Range@ 5500, achillesQ@# &] (* From Robert G. Wilson v, Jun 10 2010 *)

PROG

(PARI) isA052486(n) = { n>1 & vecmin(factor(n)[, 2])>1 & !ispower(n) } \\ From M. F. Hasler, Sep 23 2010

CROSSREFS

Cf. A001597, A001694, A007916.

Sequence in context: A102562 A216426 A072412 * A114128 A143610 A166987

Adjacent sequences:  A052483 A052484 A052485 * A052487 A052488 A052489

KEYWORD

nonn

AUTHOR

Henry Bottomley, Mar 16 2000

EXTENSIONS

Example edited by Mac Coombe (mac.coombe(AT)gmail.com), Sep 18 2010

STATUS

approved

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Last modified July 25 07:21 EDT 2014. Contains 244900 sequences.