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A019276
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Let sigma_m(n) be the result of applying the sum-of-divisors function m times to n; let m(n) = min m such that n divides sigma_m (n); let k(n) = sigma_{m(n)}(n)/n; sequence gives the megaperfect numbers n, where m(n) increases to a record.
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19
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Where records occur in A019294. a(n>=23) depend on a few probable primes.
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REFERENCES
| 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
| G. L. Cohen & H. J. J. te Riele, Iterating the Sum-of-Divisors Function
G. L. Cohen & H. J. J. te Riele, Iterating the Sum-of-Divisors Function
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MATHEMATICA
| 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}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 24 2005)
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CROSSREFS
| Cf. A019277, A019294, A019295.
Sequence in context: A157604 A101737 A176550 * A097683 A141403 A124204
Adjacent sequences: A019273 A019274 A019275 * A019277 A019278 A019279
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KEYWORD
| hard,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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