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A019276 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. 17
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; text; internal format)
OFFSET

1,2

COMMENTS

Where records occur in A019294. a(n>=23) depend on a few probable primes.

REFERENCES

Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.

LINKS

Table of n, a(n) for n=1..26.

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

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 *)

CROSSREFS

Cf. A019277, A019294, A019295.

Sequence in context: A214125 A275466 A317786 * A097683 A141403 A124204

Adjacent sequences:  A019273 A019274 A019275 * A019277 A019278 A019279

KEYWORD

hard,nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 20 20:50 EDT 2019. Contains 326155 sequences. (Running on oeis4.)