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A203663 Achilles number whose double is also an Achilles number. 0
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 a(n) is 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

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: A069781 A231231 A179666 * A250815 A006910 A015229

Adjacent sequences:  A203660 A203661 A203662 * A203664 A203665 A203666

KEYWORD

nonn,changed

AUTHOR

Antonio Roldán, Jan 04 2012

STATUS

approved

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Last modified January 21 13:38 EST 2018. Contains 297994 sequences.