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%I #25 Sep 08 2023 02:45:36
%S 1,2,3,4,6,6,18,8,9,12,108,12,1944,36,18,16,209952,18,408146688,24,54,
%T 216,85691213438976,24,36,3888,27,72,34974584955819144511488,36,
%U 2997014624388697307377363936018956288,32,324,419904,108,36,104819342594514896999066634490728502944926883876041385836544,816293376,5832,48
%N 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 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 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 Antti Karttunen, <a href="/A265399/b265399.txt">Table of n, a(n) for n = 1..60</a>
%F 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 Other identities. For all n >= 1:
%F a(n) = 2^A265752(n) * 3^A265753(n).
%t 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 (PARI)
%o \\ Needs also code from A265398.
%o A265399(n) = if(A065331(n) == n, n, A265399(A265398(n)));
%o for(n=1, 60, write("b265399.txt", n, " ", A265399(n)));
%o (Scheme) (definec (A265399 n) (if (= (A065331 n) n) n (A265399 (A265398 n))))
%Y Cf. A003586 (fixed points), A065331.
%Y Cf. also A192232, A206296, A265398, A265752, A265753.
%K nonn,easy,mult
%O 1,2
%A _Antti Karttunen_, Dec 15 2015
%E Keyword mult added by _Antti Karttunen_, Aug 04 2018
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