%I #28 Dec 27 2021 21:09:13
%S 1,2,4,6,12,16,18,30,60
%N Let sigma_m(n) be result of applying the sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m(n) = k*n; sequence gives log_2 of the (2,2)-perfect numbers.
%C Cohen and te Riele prove that any even (2,2)-perfect number (a "superperfect" number) must be of the form 2^(p-1) with 2^p-1 prime (Suryanarayana) and the converse also holds. Any odd superperfect number must be a perfect square (Kanold). Searches up to > 10^20 did not find any odd examples. - _Ralf Stephan_, Jan 16 2003
%C See also the Cohen-te Riele links under A019276.
%H Graeme L. Cohen and Herman J. J. te Riele, <a href="http://projecteuclid.org/euclid.em/1047565640">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5 (1996), pp. 93-100.
%F Coincides with A000043(n) - 1 unless odd superperfect numbers exist.
%Y Cf. A019278, A019279.
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_
%E a(8)-a(9) from _Jud McCranie_, Jun 01 2000