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
Graeme L. Cohen and Herman J. J. te Riele, Iterating the sum-of-divisors function, Experimental Mathematics, 5 (1996), pp. 93-100.
FORMULA
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
KEYWORD
hard,nonn
AUTHOR
EXTENSIONS
Definition corrected by M. F. Hasler, Jan 07 2020
STATUS
approved