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%I #33 Dec 24 2014 22:49:27
%S 3,99,168,780,1836,2976,5928,6201,6468,13888,48768,75696,123216,
%T 227584,285948,401952,437664,1003000,2058732,3302592,3810624,4031488,
%U 4258496,4318656,6713664,14188992,32021613,93298284,201302016,226196736,381144320,514882128
%N Numbers n such that sigma(n) = 4*(n-phi(n)).
%C If 2^p-1 is a prime (a Mersenne prime) greater than 3 then 3*2^p*(2^p-1) is in the sequence (the proof is easy). The sequence A110075 gives such terms of this sequence. - _Farideh Firoozbakht_, Jul 27 2005
%C If 2^p-1 is a prime (a Mersenne prime) not equal to 7 then 7*2^(p+1)*(2^p-1) is in the sequence (the proof is easy). - _Farideh Firoozbakht_, Aug 18 2013
%C Theorem: If 2^p-1 and 2^q-1 are two distinct Mersenne primes then 2^(p+q-2)*(2^p-1)*(2^q-1) is in the sequence (the proof is easy). The two preceding remarks are the special cases q = 2 and q = 3. - _Farideh Firoozbakht_, Dec 21 2014
%t a068420[n_] := Select[Range[n], DivisorSigma[1, #] == 4 (# - EulerPhi[#]) &]; a068420[10^6] (* _Michael De Vlieger_, Dec 21 2014 *)
%o (PARI) for(n=1,100000000,if(sigma(n)==4*(n-eulerphi(n)),print1(n,",")))
%Y Cf. A000668, A110075.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Mar 02 2002
%E More terms from _Rick L. Shepherd_, Apr 03 2002
%E a(29)-a(32) from _Donovan Johnson_, Jun 30 2012