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A019285
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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 (2,8)-perfect numbers.
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60, 240, 960, 4092, 16368, 58254, 61440, 65472, 116508, 466032, 710400, 983040, 1864128, 3932160, 4190208, 67043328, 119304192, 268173312, 1908867072, 7635468288, 16106127360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If 2^p-1 is a Mersenne prime greater than 3 then m = 15*2^(p-1) is in the sequence. Because sigma(sigma(m)) = sigma(15*2^(p-1)) = sigma(24*(2^p-1)) = 60*2^p = 8*(15*2^(p-1)) = 8*m. So for n>1 15/2*(A000668(n)+1) is in the sequence. 60, 240, 960, 61440, 983040, 3932160, 16106127360 and 1729382256910270464042 are such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 05 2005
See also the Cohen-te Reile links under A019276.
No other terms < 5x10^11. - 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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CROSSREFS
| Cf. A000668.
Sequence in context: A075287 A103741 A140873 * A206144 A008428 A206232
Adjacent sequences: A019282 A019283 A019284 * A019286 A019287 A019288
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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
| One more term from Jud McCranie, Nov 13 2001, and a(20) and a(21) Jan 2012
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