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A019276
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.
18
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
OFFSET
1,2
COMMENTS
Where records occur in A019294. a(n>=23) depend on a few probable primes.
LINKS
Graeme L. Cohen & Herman J. J. te Riele, Iterating the Sum-of-Divisors Function: Abstract. (Page no longer available; link gives latest snapshot on web.archive.org from Sept. 2006)
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.]
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.
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}] (* Robert G. Wilson v, Jun 24 2005 *)
PROG
(PARI) m=0; for(n=1, oo, m<(m=max(A019294(n), m))&&print1(n", ")) \\ M. F. Hasler, Jan 07 2020
CROSSREFS
Cf. A019277 (the record values), A019294 (min{m: n|sigma^(m)(n)}), A019295 (ratio sigma^(m)(n)/n).
Sequence in context: A214125 A275466 A317786 * A097683 A334264 A141403
KEYWORD
hard,nonn
STATUS
approved