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Numbers n such that sigma(n) - n = perfect number (A000396).
1

%I #18 Mar 12 2014 17:16:00

%S 6,25,28,496,652,8128,10682,10828,33550336,44655764,8589869056,

%T 8623554304,137438691328

%N Numbers n such that sigma(n) - n = perfect number (A000396).

%C Also numbers n such that sum of the proper divisors of n (A001065) = perfect number (A000396).

%C Supersequence of perfect numbers (A000396).

%C a(14) > 10^12. - _Giovanni Resta_, Mar 01 2014

%C Up to a(13), note that the terms that are not perfect are deficient. - _Michel Marcus_, Mar 12 2014

%e Number 25 is a term because sigma(25) - 25 = 31 - 25 = 6 (perfect number).

%o (PARI) isok(n) = sigma(smn=sigma(n) - n) == 2*smn; \\ _Michel Marcus_, Mar 01 2014

%Y Cf. A000203 (sigma(n)).

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Feb 28 2014

%E a(10) from _Michel Marcus_, Mar 01 2014

%E a(11)-a(13) from _Giovanni Resta_, Mar 01 2014