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A097248
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a(n) is the eventual stable point reached when iterating k -> A097246(k), starting from k = n.
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19
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1, 2, 3, 3, 5, 6, 7, 6, 5, 10, 11, 5, 13, 14, 15, 5, 17, 10, 19, 15, 21, 22, 23, 10, 7, 26, 15, 21, 29, 30, 31, 10, 33, 34, 35, 15, 37, 38, 39, 30, 41, 42, 43, 33, 7, 46, 47, 15, 11, 14, 51, 39, 53, 30, 55, 42, 57, 58, 59, 7, 61, 62, 35, 15, 65, 66, 67, 51, 69, 70, 71, 30, 73, 74, 21
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OFFSET
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1,2
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COMMENTS
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a(n) = r(n,m) with m such that r(n,m)=r(n,m+1), where r(n,k) = A097246(r(n,k-1)), r(n,0)=n. (The original definition.)
The above remark could be interpreted to mean that A097249(n) <= a(n).
All terms are squarefree, and the squarefree numbers are the fixed points.
These are also fixed points eventually reached when iterating A277886.
(End)
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LINKS
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FORMULA
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If A008683(n) <> 0 [when n is squarefree], a(n) = n, otherwise a(n) = a(A097246(n)).
(End)
a(1) = 1; a(p) = p, for prime p; a(m*k) = A331590(a(m), a(k)).
(End)
(End)
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MATHEMATICA
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Table[FixedPoint[Times @@ Map[#1^#2 & @@ # &, Partition[#, 2, 2] &@ Flatten[FactorInteger[#] /. {p_, e_} /; e >= 2 :> {If[OddQ@ e, {p, 1}, {1, 1}], {NextPrime@ p, Floor[e/2]}}]] &, n], {n, 75}] (* Michael De Vlieger, Mar 18 2017 *)
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PROG
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(PARI)
A097246(n) = { my(f=factor(n)); prod(i=1, #f~, (nextprime(f[i, 1]+1)^(f[i, 2]\2))*((f[i, 1])^(f[i, 2]%2))); };
(Scheme) ;; with memoization-macro definec
;; Two implementations:
(Python)
from sympy import factorint, nextprime
from operator import mul
def a097246(n):
f=factorint(n)
return 1 if n==1 else reduce(mul, [(nextprime(i)**int(f[i]/2))*(i**(f[i]%2)) for i in f])
def a(n):
k=a097246(n)
while k!=n:
n=k
k=a097246(k)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Name changed and the original definition moved to the Comments section by Antti Karttunen, Nov 15 2016
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STATUS
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approved
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