%I #35 Feb 19 2024 10:28:25
%S 1,4,56,7192,7232,7912,10792,17272,30592,114256,2154584,3428368,
%T 44375136,89245784,2739393699744
%N Numbers n such that n divides sigma(n) - d(n).
%C Or, numbers n such that sigma(n) = k*n + d(n) for some k.
%C For most terms > 4, sigma(n) = 2*n + d(n), i.e., k=2. However, for the 12th term, k=3.
%C If p = 2^m-(2m+1) is prime and n = 2^(m-1)*p then sigma(n) = 2*n+d(n), i.e., k=2 and n is in the sequence. 56, 7232, 30592, 36028789368553472, 9223371897268338688 and 29230032746618058364071726105239688547563879792624 are such terms of the sequence. - _Farideh Firoozbakht_, Aug 19 2013
%C a(16) > 8*10^12. - _Giovanni Resta_, Nov 07 2019
%H Farideh Firoozbakht and M. F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for perfect numbers</a>, Journal of Integer Sequences 13.3 (2010), 18 pp. Article ID 10.3.1.
%F Numbers n such that A000203(n) (mod n) == A000005(n) or A054024(n)=A000005(n). - _Labos Elemer_, Apr 12 2002
%t Do[If[Mod[DivisorSigma[1, n]-DivisorSigma[0, n], n]==0, Print[n]], {n, 1, 10^8}]
%o (PARI) is(n)=my(f=factor(n)); (sigma(f)-numdiv(f))%n==0 \\ _Charles R Greathouse IV_, Nov 04 2016
%Y Cf. A000203, A000005, A054024.
%K nonn,more
%O 1,2
%A _Robert G. Wilson v_, Jul 26 2000
%E a(15) from _Giovanni Resta_, Nov 07 2019