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A019277 Records in A019294, number of iterations of the sigma function to reach a multiple of the starting value. 5
1, 2, 4, 5, 7, 15, 16, 17, 78, 97, 101, 120, 174, 214, 239, 261, 263, 296, 380, 557, 1287, 1524, 1722, 1911, 2023, 2373 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Original name: 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 k(n) for the megaperfect numbers n, where m(n) increases.

Records in A019294. a(n>=23) depend on a few probable primes.

See also the Cohen-te Riele links under A019276.

The original name mentioned the sequence of ratios k, i.e., A019295(A019276) = (1, 2, 5, 24, 168, 1834560, 6516224, 881280, ...), at present not listed in the OEIS. - M. F. Hasler, Jan 07 2020

LINKS

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

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

FORMULA

a(n) = A019294(A019276(n)). - M. F. Hasler, Jan 07 2020

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[ a]], {n, 460}] (* Robert G. Wilson v, Jun 24 2005 *)

PROG

(PARI) {M=0; for(n=1, oo, my(s=n, m=1); while((s=sigma(s))%n, m++); m>M&&print1(M=m, ", "))} \\ M. F. Hasler, Jan 07 2020

CROSSREFS

Cf. A019276 (megaperfect numbers: where A019294 has records), A019294 (min m: n|sigma^m(n)), A019295 (sigma^m(n)/n with m = A019294).

Sequence in context: A063508 A101724 A123210 * A127791 A290431 A220701

Adjacent sequences:  A019274 A019275 A019276 * A019278 A019279 A019280

KEYWORD

hard,nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Definition corrected by M. F. Hasler, Jan 07 2020

STATUS

approved

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)