OFFSET
1,4
COMMENTS
The table of trajectories of n under is given in A329288.
All fixed points, besides 1, are prime.
Conjecture: every number appears in the sequence infinitely many times.
Conjecture: all terms are nonzero, i.e., every trajectory eventually reaches a prime.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(p) = 1 for any prime number p.
EXAMPLE
For n = 26 the trajectory is (26, 27, 35, 39, 41) so a(26) = 5.
MAPLE
g:= n -> n - 1 + n/max(numtheory:-factorset(n)):
f:= proc(n) option remember;
if isprime(n) then 1 else 1+ procname(g(n)) fi
end proc:
f(1):= 1:
map(f, [$1..200]); # Robert Israel, May 01 2020
MATHEMATICA
Clear[f, it, order, seq]; f[n_]:=f[n]=n-1+n/FactorInteger[n][[-1]][[1]]; it[k_, n_]:=it[k, n]=f[it[k, n-1]]; it[k_, 1]=k; order[n_]:=order[n]=SelectFirst[Range[1, 100], it[n, #]==it[n, #+1]&]; Print[order/@Range[1, 100]];
PROG
(PARI) apply( {a(n, c=1)=n>1&&while(n<n+=n/vecmax(factor(n)[, 1])-1, c++); c}, [1..99]) \\ M. F. Hasler, Feb 19 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Elijah Beregovsky, Feb 16 2020
STATUS
approved