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Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,3)-perfect numbers.
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%I #23 Sep 29 2023 22:03:02

%S 8,21,512

%N Let sigma_m (n) be result of applying sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m (n) = k*n; sequence gives the (2,3)-perfect numbers.

%C See also the Cohen-te Riele links under A019276.

%C No further term < 10^9 [see Table 1].

%C No other terms < 5*10^11. - _Jud McCranie_, Feb 08 2012

%C a(4) > 4*10^12, if it exists. - _Giovanni Resta_, Feb 26 2020

%H Graeme L. Cohen and Herman J. J. te Riele, <a href="http://www.emis.de/journals/EM/expmath/volumes/5/5.html">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5 (1996), pp. 93-100.

%H Experimental Mathematics, <a href="http://www.emis.de/journals/EM/">Home Page</a>.

%Y Cf. A019278, A019279, A019282, A019283, A019284, A019285, A019286, A019287, A019288, A019289, A019290, A019291.

%K nonn,bref,more

%O 1,1

%A _N. J. A. Sloane_