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A203663 Achilles number whose double is also an Achilles number. 1
432, 972, 1944, 2000, 2700, 3456, 4500, 5292, 5400, 5488, 8748, 9000, 10584, 10800, 12348, 12500, 13068, 15552, 16000, 17496, 18000, 18252, 21168, 21296, 21600, 24300, 24500, 24696, 25000, 26136 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Every term is a multiple of 4.
LINKS
EXAMPLE
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.
MAPLE
filter:= proc(n) local e2, F;
e2:= padic:-ordp(n, 2);
if e2 < 2 then return false fi;
F:= map(t -> t[2], ifactors(n/2^e2)[2]);
min(F) > 1 and igcd(e2, op(F))=1 and igcd(e2+1, op(F))=1
end proc:
select(filter, [seq(i, i=4..10^5, 4)]); # Robert Israel, Jan 16 2018
MATHEMATICA
achillesQ[n_] := With[{ee = FactorInteger[n][[All, 2]]}, Min[ee] > 1 && GCD@@ee == 1];
Select[Range[4, 10^5, 4], achillesQ[#] && achillesQ[2#]&] (* Jean-François Alcover, Sep 25 2020 *)
PROG
(PARI) achilles(n) = { n>1 & vecmin(factor(n)[, 2])>1 & !ispower(n) } \\ M. F. Hasler, 2010
{ for (n=1, 10^6, if (achilles(n)==1 && achilles(2*n)==1, print1(n, ", "))); } \\ Antonio Roldán, Oct 07 2012
CROSSREFS
Sequence in context: A337670 A231231 A179666 * A250815 A006910 A015229
KEYWORD
nonn
AUTHOR
Antonio Roldán, Jan 04 2012
STATUS
approved

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Last modified April 22 22:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)