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Search: id:A019283
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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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| 42, 84, 160, 336, 1344, 86016, 550095, 1376256, 5505024
(list; graph; listen)
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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 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.
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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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MATHEMATICA
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Do[If[DivisorSigma[1, DivisorSigma[1, n]]==6n, Print[n]], {n, 6000000}] (Firoozbakht)
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CROSSREFS
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Cf. A000668.
Sequence in context: A135850 A153644 A160283 this_sequence A067296 A044180 A044561
Adjacent sequences: A019280 A019281 A019282 this_sequence A019284 A019285 A019286
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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