OFFSET
1,3
COMMENTS
A preliminary for investigating iterates of A206369.
REFERENCES
See A206369.
FORMULA
a(1) = 0; for n > 1, a(n) = 1 + a(A206369(n)).
EXAMPLE
Iterating A206369 with a starting value of 27 gives 20, 12, 6, 2, 1, taking 5 steps to reach 1. So a(27) = 5.
MATHEMATICA
f[p_, e_] := Sum[(-1)^(e-k)*p^k, {k, 0, e}]; s[1] = 1; s[n_] := Times @@ (f @@@ FactorInteger[n]); a[n_] := Length @ FixedPointList[s, n] - 2; Array[a, 90] (* Amiram Eldar, Jan 01 2020 *)
PROG
(PARI) f(n) = sumdiv(n, d, eulerphi(n/d) * issquare(d)); \\ A206369
a(n) = {if (n==1, return (0)); my(nb = 1); while ((n = f(n)) != 1, nb++); nb; } \\ Michel Marcus, Jan 01 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Allan C. Wechsler, Dec 31 2019
STATUS
approved