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A019283
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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 (2,6)-perfect numbers.
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OFFSET
| 1,1
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COMMENTS
| If 2^p-1 is a Mersenne prime then m = 21*2^(p-1) is in the sequence. Because sigma(sigma(m)) = 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 (mymontain(AT)yahoo.com), Dec 05 2005
See also the Cohen-te Reile links under A019276.
No other terms < 5 x 10^11. - Jud McCranie, Feb 08 2012
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REFERENCES
| Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.
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LINKS
| Experimental Mathematics, Home Page
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MATHEMATICA
| Do[If[DivisorSigma[1, DivisorSigma[1, n]]==6n, Print[n]], {n, 6000000}] (Firoozbakht)
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CROSSREFS
| Cf. A000668.
Sequence in context: A153644 A172437 A160283 * A067296 A044180 A044561
Adjacent sequences: A019280 A019281 A019282 * A019284 A019285 A019286
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(10) by Jud McCranie, Feb 08 2012
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