A068414 - OEIS

%I #25 May 14 2022 11:30:08

%S 1,12,56,260,992,1976,2156,2754,16256,25232,41072,133984,145888,

%T 1100864,1270208,1439552,2237888,4729664,67100672,75398912,171627376,

%U 277060144,473089984,538178048,558585344,629225984,1192258048,1863840112,2181070592,4534854656

%N Numbers k such that sigma(k) = 3k - 2*phi(k).

%C If 2^p-1 is prime (a Mersenne prime) and n = 2^p*(2^p-1) then n is in the sequence because 3*n-2*phi(n) = 3*2^p*(2^p-1)-2^p*(2^p-2) = 2^p*(2^(p+1)-1) = sigma(2^p-1)*sigma(2^p) = sigma(2^p*(2^p-1)) = sigma(n). - _Farideh Firoozbakht_, Dec 31 2005

%t Select[Range[10^6], DivisorSigma[1, #] == 3*# - 2*EulerPhi[#] &] (* _Amiram Eldar_, May 14 2022 *)

%o (PARI) for(n=1,500000, if(sigma(n)==3*n-2*eulerphi(n),print1(n,",")))

%Y Cf. A000010, A000203, A068418, A069719, A069737.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Mar 03 2002

%E More terms (complete up to 50000000). - _Rick L. Shepherd_, Mar 28 2002

%E More terms from _Labos Elemer_, Apr 03 2002

%E a(24)-a(30) from _Donovan Johnson_, Feb 08 2012