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A019284 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 (2,7)-perfect numbers. 13

%I #45 Feb 27 2020 04:34:30

%S 24,1536,47360,343976,572941926400

%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 (2,7)-perfect numbers.

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

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

%C 572941926400 is also a term. See comment in A019278. - _Michel Marcus_, May 15 2016

%C a(6) > 4*10^12, if it exists. - _Giovanni Resta_, Feb 26 2020

%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.

%t Select[Range[50000], DivisorSigma[1, DivisorSigma[1, #]]/# == 7 &] (* _Robert Price_, Apr 07 2019 *)

%o (PARI) isok(n) = sigma(sigma(n))/n == 7; \\ _Michel Marcus_, May 12 2016

%Y Cf. A000668, A019278, A019279, A019281, A019282, A019283, A019285, A019286, A019287, A019288, A019289, A019290, A019291.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_

%E a(5) from _Giovanni Resta_, Feb 26 2020

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Last modified April 19 11:14 EDT 2024. Contains 371791 sequences. (Running on oeis4.)