cp's OEIS Frontend

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.

%I A019276 #25 Jan 10 2020 13:12:43
%S A019276 1,2,3,5,9,11,23,25,29,59,67,101,131,173,202,239,353,389,401,461,659,
%T A019276 1319,1579,1847,2309,2797
%N 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.
%C A019276 Where records occur in A019294. a(n>=23) depend on a few probable primes.
%H A019276 Graeme L. Cohen & Herman J. J. te Riele, <a href="http://web.archive.org/db.cwi.nl/rapporten/abstract.php?abstractnr=897">Iterating the Sum-of-Divisors Function</a>: Abstract. (Page no longer available; link gives latest snapshot on web.archive.org from Sept. 2006)
%H A019276 Graeme L. Cohen & Herman J. J. te Riele, <a href="http://repos.project.cwi.nl:8888/cwi_repository/docs/I/10/10355A.pdf">Iterating the Sum-of-Divisors Function</a> [Broken link to a file "10355A.pdf", maybe the same as NM-R9525.pdf available through the above page of abstract.]
%H A019276 Graeme L. Cohen and Herman J. J. te Riele, <a href="https://projecteuclid.org/euclid.em/1047565640">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5 (1996), pp. 93-100.
%t A019276 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 *)
%o A019276 (PARI) m=0;for(n=1,oo,m<(m=max(A019294(n),m))&&print1(n",")) \\ _M. F. Hasler_, Jan 07 2020
%Y A019276 Cf. A019277 (the record values), A019294 (min{m: n|sigma^(m)(n)}), A019295 (ratio sigma^(m)(n)/n).
%K A019276 hard,nonn
%O A019276 1,2
%A A019276 _N. J. A. Sloane_