

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.


6



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

1,2


COMMENTS

In terms of integers: apply A265398 as many times as necessary to n, until it gets 3smooth, one of the terms of A003586.
Completely multiplicative with a(2) = 2, a(3) = 3, a(p) = a(A265398(p)) for p > 3.  Andrew Howroyd & Antti Karttunen, Aug 04 2018


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..60


FORMULA

If A065331(n) = n [that is, when n is one of 3smooth numbers, A003586] then a(n) = n, otherwise a(n) = a(A265398(n)).
Other identities. For all n >= 1:
a(n) = 2^A265752(n) * 3^A265753(n).


PROG

(PARI)
\\ Needs also code from A265398.
A265399(n) = if(A065331(n) == n, n, A265399(A265398(n)));
for(n=1, 60, write("b265399.txt", n, " ", A265399(n)));
(Scheme) (definec (A265399 n) (if (= (A065331 n) n) n (A265399 (A265398 n))))


CROSSREFS

Cf. A003586 (fixed points), A065331.
Cf. also A192232, A206296, A265398, A265752, A265753.
Sequence in context: A265398 A299438 A030209 * A138588 A143102 A013944
Adjacent sequences: A265396 A265397 A265398 * A265400 A265401 A265402


KEYWORD

nonn,mult


AUTHOR

Antti Karttunen, Dec 15 2015


EXTENSIONS

Keyword mult added by Antti Karttunen, Aug 04 2018


STATUS

approved



