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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. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In terms of integers: apply A265398 as many times as necessary to n, until it gets 3-smooth, 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 3-smooth 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

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Last modified February 23 06:13 EST 2020. Contains 332159 sequences. (Running on oeis4.)