OFFSET
1,1
COMMENTS
Every term is a multiple of 4.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..4148 from Robert Israel)
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
(Python)
# uses program in A052486
from itertools import count, islice
from math import gcd
from sympy import factorint
def A203663_gen(): # generator of terms
return map(lambda x:x[0], filter(lambda x:all(d>1 for d in x[1]) and gcd(*x[1])==1, map(lambda x: (x, factorint(x<<1).values()), (A052486(i) for i in count(1)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio Roldán, Jan 04 2012
STATUS
approved