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A068412
Composite numbers k such that phi(k) divides sigma(k) - 2*k.
1
6, 12, 28, 42, 60, 168, 456, 496, 828, 1080, 1242, 1530, 1560, 3360, 3672, 4560, 7320, 7584, 8128, 11400, 14784, 19488, 21648, 33462, 37536, 40608, 44856, 48024, 59520, 83904, 87648, 221088, 352704, 354384, 560664, 613440, 1288224, 1365984, 1420320, 1482480
OFFSET
1,1
COMMENTS
The first four numbers in this sequence {6, 12, 28, 42} are featured in the cult film "Donnie Darko", in which the title character is warned that the world will end in 28 days, 6 hours, 42 minutes and 12 seconds. - Don Rogers (donrogers42(AT)aol.com), Sep 21 2006
LINKS
MAPLE
select(t -> not isprime(t) and (numtheory:-sigma(t) - 2*t) mod numtheory:-phi(t) = 0, [$4..2*10^6]); # Robert Israel, Jan 15 2017
MATHEMATICA
Select[Range[15*10^5], CompositeQ[#]&&Divisible[DivisorSigma[1, #]-2#, EulerPhi[ #]]&] (* Harvey P. Dale, Mar 08 2023 *)
PROG
(PARI) for(n=2, 300000, if((sigma(n)-2*n)%(eulerphi(n))==isprime(n), print1(n, ", ")))
(PARI) is(n) = {my(f = factor(n)); !((sigma(f) - 2*n) % (eulerphi(f))); } \\ Amiram Eldar, Feb 01 2024
CROSSREFS
Includes A000396.
Sequence in context: A086792 A064987 A057341 * A183026 A146005 A325812
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Mar 03 2002
EXTENSIONS
More terms from Rick L. Shepherd, Apr 08 2002
STATUS
approved