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Start with n and repeatedly apply the map x -> A087207(x) until we reach 0; a(n) is the number of steps needed, or -1 if 0 is never reached.
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%I #28 Aug 15 2023 10:08:38

%S 1,2,3,2,3,4,3,2,3,4,3,4,3,4,5,2,3,4,3,4,5,4,3,4,3,6,3,4,3,4,3,2,5,6,

%T 5,4,3

%N Start with n and repeatedly apply the map x -> A087207(x) until we reach 0; a(n) is the number of steps needed, or -1 if 0 is never reached.

%C There is a conjecture that 0 is always reached - see A087207.

%H Robert Israel, <a href="/A288569/a288569.txt">Table of n, a(n) for n = 1..10000</a>. If a(n) is not known, it is given in the form k + a(x). [A large file]

%e 10 -> 5 -> 4 -> 1 -> 0 reaches 0 in 4 steps, so a(10)=4.

%e 38 = 2*19 -> 129 = 3*43 -> 8194 = 2*17*241 -> 4503599627370561 = 3^2*37*71*190483425427 -> ..., and a(38) is presently unknown.

%p f:= proc(n) local i; option remember;

%p add(2^(numtheory:-pi(t)-1), t = numtheory:-factorset(n)) end proc:

%p g:= proc(n) local t,count;

%p t:= n;

%p for count from 0 while t <> 0 do

%p t:= f(t)

%p od;

%p count

%p end proc:

%p map(g, [$1..37]); # _Robert Israel_, Jun 25 2017

%t f[n_] := Total[2^(PrimePi /@ FactorInteger[n][[All, 1]]-1)]; f[1] = 0;

%t g[n_] := Module[{t, count}, t = n; For[count = 0, t != 0, count++, t = f[t]]; count];

%t Table[g[n], {n, 1, 37}] (* _Jean-François Alcover_, Aug 15 2023, after _Robert Israel_ *)

%o (Python)

%o from sympy import factorint, primepi

%o def f(n):

%o return 0 if n < 2 else sum(1 << int(primepi(i-1)) for i in factorint(n))

%o def a(n):

%o fn, c = n, 0

%o while not fn == 0: fn, c = f(fn), c+1

%o return c

%o print([a(n) for n in range(1, 38)]) # _Michael S. Branicky_, Jul 11 2022

%Y Cf. A087207.

%K nonn,more,hard

%O 1,2

%A _N. J. A. Sloane_, Jun 25 2017