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Search: id:A019280
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| A019280 |
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Let sigma_m(n) be result of applying the sum-of-divisors function m times to n; call n (m,k)-perfect if sigma_m(n) = k*n; sequence gives log_2 of the (2,2)-perfect numbers. |
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2
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OFFSET
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1,2
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COMMENT
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Cohen and te Riele prove that any even (2,2)-perfect number (a "superperfect" number) must be of the form 2^(p-1) with 2^p-1 prime (Suryanarayana) and the converse also holds. Any odd superperfect number must be a perfect square (Kanold). Searches up to >10^20 did not find any odd examples. - Ralf Stephan, Jan 16 2003
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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G. L. Cohen & H. J. J. te Riele, Iterating the Sum-of-Divisors Function
Experimental Mathematics, Home Page
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FORMULA
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Coincides with A000043(n) - 1 unless odd superperfect numbers exist.
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CROSSREFS
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Cf. A019279.
Sequence in context: A013916 A141113 A050584 this_sequence A090748 A032465 A089395
Adjacent sequences: A019277 A019278 A019279 this_sequence A019281 A019282 A019283
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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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EXTENSIONS
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2 more terms sent by Jud McCranie (j.mccranie(AT)comcast.net), Jun 01 2000
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