A203663 Achilles number whose double is also an Achilles number.

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

Offset

1,1

Comments

Every term is a multiple of 4.

Links

Robert Israel, Table of n, a(n) for n = 1..4148

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

Cf. A052486, A143610, A203662.

Sequence in context: A337670 A231231 A179666 * A250815 A006910 A015229

Adjacent sequences: A203660 A203661 A203662 * A203664 A203665 A203666

Keyword

nonn

Author

Antonio Roldán, Jan 04 2012

Status

approved