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Search: id:A019285
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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
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OFFSET
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1,1
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COMMENT
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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 (f.firoozbakht(AT)math.ui.ac.ir), Dec 05 2005
See also the Cohen-te Reile links under A019276.
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REFERENCES
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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
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Experimental Mathematics, Home Page
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CROSSREFS
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Cf. A000668.
Adjacent sequences: A019282 A019283 A019284 this_sequence A019286 A019287 A019288
Sequence in context: A075287 A103741 A140873 this_sequence A008428 A075295 A134587
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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One more term from Jud McCranie (j.mccranie(AT)comcast.net), Nov 13 2001. No other terms < 4290000000.
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