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 A019283 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 (2,6)-perfect numbers. 6
 42, 84, 160, 336, 1344, 86016, 550095, 1376256, 5505024, 22548578304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If 2^p-1 is a Mersenne prime then m = 21*2^(p-1) is in the sequence. Because sigma(sigma(m)) = sigma(sigma(21*2^(p-1))) = sigma(32*(2^p-1)) = 63*2^p = 6*(21*2^(p-1)) = 6*m. So 21*(A000668+1)/2 is a subsequence of this sequence. This is the subsequence 42, 84, 336, 1344, 86016, 1376256, 5505024, 22548578304, 24211351596743786496, ... - Farideh Firoozbakht, Dec 05 2005 See also the Cohen-te Riele links under A019276. No other terms < 5 * 10^11. - Jud McCranie, Feb 08 2012 Any odd perfect numbers must occur in this sequence, as such numbers must be in the intersection of A000396 and A326051, that is, satisfy both sigma(n) = 2n and sigma(2n) = 6n, thus in combination they must satisfy sigma(sigma(n)) = 6n. Note that any odd perfect number should occur also in A326181. - Antti Karttunen, Jun 16 2019 LINKS Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100. MATHEMATICA Do[If[DivisorSigma[1, DivisorSigma[1, n]]==6n, Print[n]], {n, 6000000}] (* Farideh Firoozbakht, Dec 05 2005 *) PROG (PARI) isok(n) = sigma(sigma(n))/n  == 6; \\ Michel Marcus, May 12 2016 CROSSREFS Cf. A000668, A019278, A019279, A019282. Cf. A000203, A000396, A005820, A051027, A326051, A326181. Sequence in context: A172437 A160283 A325994 * A300603 A301328 A067296 Adjacent sequences:  A019280 A019281 A019282 * A019284 A019285 A019286 KEYWORD nonn,more AUTHOR EXTENSIONS a(10) by Jud McCranie, Feb 08 2012 STATUS approved

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Last modified October 15 21:17 EDT 2019. Contains 328038 sequences. (Running on oeis4.)