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Composite numbers k such that phi(k) divides sigma(k) - 2*k.
1

%I #25 Feb 01 2024 01:34:02

%S 6,12,28,42,60,168,456,496,828,1080,1242,1530,1560,3360,3672,4560,

%T 7320,7584,8128,11400,14784,19488,21648,33462,37536,40608,44856,48024,

%U 59520,83904,87648,221088,352704,354384,560664,613440,1288224,1365984,1420320,1482480

%N Composite numbers k such that phi(k) divides sigma(k) - 2*k.

%C 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

%H Amiram Eldar, <a href="/A068412/b068412.txt">Table of n, a(n) for n = 1..104</a>

%p 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

%t Select[Range[15*10^5],CompositeQ[#]&&Divisible[DivisorSigma[1,#]-2#,EulerPhi[ #]]&] (* _Harvey P. Dale_, Mar 08 2023 *)

%o (PARI) for(n=2,300000, if((sigma(n)-2*n)%(eulerphi(n))==isprime(n),print1(n,",")))

%o (PARI) is(n) = {my(f = factor(n)); !((sigma(f) - 2*n) % (eulerphi(f)));} \\ _Amiram Eldar_, Feb 01 2024

%Y Includes A000396.

%Y Cf. A000010, A000203, A033880.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Mar 03 2002

%E More terms from _Rick L. Shepherd_, Apr 08 2002