login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 12
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

COMMENTS

Number of terms < 10^n: 0, 1, 13, 60, 252, 916, 3158, 10553, 34561, 111891, 359340, 1148195, 3656246, 11616582, 36851965, ..., A118896(n) - A070428(n). - Robert G. Wilson v, Aug 11 2014

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.

MAPLE

filter:= proc(n) local E; E:= map(t->t[2], ifactors(n)[2]); min(E)>1 and igcd(op(E))=1 end proc:

select(filter, [$1..10000]); # Robert Israel, Aug 11 2014

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 01:41 EST 2014. Contains 250286 sequences.