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A265399 Repeatedly perform x^2 -> x+1 reduction for polynomial (with nonnegative integer coefficients) encoded in prime factorization of n, until the polynomial is at most degree 1.

%I A265399 #25 Sep 08 2023 02:45:36
%S A265399 1,2,3,4,6,6,18,8,9,12,108,12,1944,36,18,16,209952,18,408146688,24,54,
%T A265399 216,85691213438976,24,36,3888,27,72,34974584955819144511488,36,
%U A265399 2997014624388697307377363936018956288,32,324,419904,108,36,104819342594514896999066634490728502944926883876041385836544,816293376,5832,48
%N A265399 Repeatedly perform x^2 -> x+1 reduction for polynomial (with nonnegative integer coefficients) encoded in prime factorization of n, until the polynomial is at most degree 1.
%C A265399 In terms of integers: apply A265398 as many times as necessary to n, until it gets 3-smooth, one of the terms of A003586.
%C A265399 Completely multiplicative with a(2) = 2, a(3) = 3, a(p) = a(A265398(p)) for p > 3. - _Andrew Howroyd_ & _Antti Karttunen_, Aug 04 2018
%H A265399 Antti Karttunen, <a href="/A265399/b265399.txt">Table of n, a(n) for n = 1..60</a>
%F A265399 If A065331(n) = n [that is, when n is one of 3-smooth numbers, A003586] then a(n) = n, otherwise a(n) = a(A265398(n)).
%F A265399 Other identities. For all n >= 1:
%F A265399 a(n) = 2^A265752(n) * 3^A265753(n).
%t A265399 f[p_, e_] := If[p < 5, p, a[NextPrime[p, -1] * NextPrime[p, -2]]]^e; a[1] = 1; a[n_] := a[n] = Times @@ f @@@ FactorInteger[n]; Array[a, 40] (* _Amiram Eldar_, Sep 07 2023 *)
%o A265399 (PARI)
%o A265399 \\ Needs also code from A265398.
%o A265399 A265399(n) = if(A065331(n) == n, n, A265399(A265398(n)));
%o A265399 for(n=1, 60, write("b265399.txt", n, " ", A265399(n)));
%o A265399 (Scheme) (definec (A265399 n) (if (= (A065331 n) n) n (A265399 (A265398 n))))
%Y A265399 Cf. A003586 (fixed points), A065331.
%Y A265399 Cf. also A192232, A206296, A265398, A265752, A265753.
%K A265399 nonn,easy,mult
%O A265399 1,2
%A A265399 _Antti Karttunen_, Dec 15 2015
%E A265399 Keyword mult added by _Antti Karttunen_, Aug 04 2018