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 A330437 Length of trajectory of n under the map n -> n - 1 + n/gpf(n) or 0 if no fixed point is reached, where gpf(n) is the greatest prime factor of n. 4
 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 5, 4, 2, 1, 4, 1, 2, 4, 4, 3, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 3, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 2, 1, 3, 2, 4, 3, 2, 1, 2, 2, 2, 1, 4, 1, 3, 2, 2, 2, 2, 1, 4, 2, 2, 1, 4, 2, 3, 2, 4, 1, 2, 2, 4, 4, 4, 3, 2, 1, 3, 2, 4 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 17 18:03 EDT 2024. Contains 375990 sequences. (Running on oeis4.)