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%I #29 Sep 25 2020 08:41:05
%S 432,972,1944,2000,2700,3456,4500,5292,5400,5488,8748,9000,10584,
%T 10800,12348,12500,13068,15552,16000,17496,18000,18252,21168,21296,
%U 21600,24300,24500,24696,25000,26136
%N Achilles number whose double is also an Achilles number.
%C Every term is a multiple of 4.
%H Robert Israel, <a href="/A203663/b203663.txt">Table of n, a(n) for n = 1..4148</a>
%e 15552 is in the sequence because 15552 = 2^6*3^5 (Achilles number) and 15552*2 = 2^7*3^5 is also an Achilles number.
%p filter:= proc(n) local e2,F;
%p e2:= padic:-ordp(n,2);
%p if e2 < 2 then return false fi;
%p F:= map(t -> t[2], ifactors(n/2^e2)[2]);
%p min(F) > 1 and igcd(e2,op(F))=1 and igcd(e2+1,op(F))=1
%p end proc:
%p select(filter, [seq(i,i=4..10^5,4)]); # _Robert Israel_, Jan 16 2018
%t achillesQ[n_] := With[{ee = FactorInteger[n][[All, 2]]}, Min[ee] > 1 && GCD@@ee == 1];
%t Select[Range[4, 10^5, 4], achillesQ[#] && achillesQ[2#]&] (* _Jean-François Alcover_, Sep 25 2020 *)
%o (PARI) achilles(n) = { n>1 & vecmin(factor(n)[, 2])>1 & !ispower(n) } \\ _M. F. Hasler_, 2010
%o { for (n=1, 10^6, if (achilles(n)==1 && achilles(2*n)==1, print1(n,", "))); } \\ _Antonio Roldán_, Oct 07 2012
%Y Cf. A052486, A143610, A203662.
%K nonn
%O 1,1
%A _Antonio Roldán_, Jan 04 2012
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