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A265399
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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.
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6
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1, 2, 3, 4, 6, 6, 18, 8, 9, 12, 108, 12, 1944, 36, 18, 16, 209952, 18, 408146688, 24, 54, 216, 85691213438976, 24, 36, 3888, 27, 72, 34974584955819144511488, 36, 2997014624388697307377363936018956288, 32, 324, 419904, 108, 36, 104819342594514896999066634490728502944926883876041385836544, 816293376, 5832, 48
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OFFSET
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1,2
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COMMENTS
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In terms of integers: apply A265398 as many times as necessary to n, until it gets 3-smooth, one of the terms of A003586.
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LINKS
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FORMULA
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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)).
Other identities. For all n >= 1:
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MATHEMATICA
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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 *)
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PROG
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(PARI)
for(n=1, 60, write("b265399.txt", n, " ", A265399(n)));
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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