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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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1
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OFFSET
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1,2
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COMMENTS
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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 Riele links under A019276.
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LINKS
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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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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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