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A019276
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Megaperfect numbers: numbers n where A019294(n) = min {m: n divides sigma^(m) (n)} increases to a record; sigma^(m) means apply the sum-of-divisors function m times.
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18
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1, 2, 3, 5, 9, 11, 23, 25, 29, 59, 67, 101, 131, 173, 202, 239, 353, 389, 401, 461, 659, 1319, 1579, 1847, 2309, 2797
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OFFSET
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1,2
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COMMENTS
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Where records occur in A019294. a(n>=23) depend on a few probable primes.
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LINKS
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Graeme L. Cohen & Herman J. J. te Riele, Iterating the Sum-of-Divisors Function [Broken link to a file "10355A.pdf", maybe the same as NM-R9525.pdf available through the above page of abstract.]
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MATHEMATICA
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f[n_, m_] := Block[{d = DivisorSigma[1, n]}, If[Mod[d, m] == 0, 0, d]]; g[n_] := Length[ NestWhileList[ f[ #, n] &, n, # != 0 &]] - 1; a = 0; Do[b = g[n]; If[b > a, a = b; Print[ n]], {n, 460}] (* Robert G. Wilson v, Jun 24 2005 *)
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PROG
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CROSSREFS
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KEYWORD
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hard,nonn
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AUTHOR
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STATUS
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approved
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