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A322027
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Maximum order of primeness among the prime factors of n; a(1) = 0.
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4
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0, 1, 2, 1, 3, 2, 1, 1, 2, 3, 4, 2, 1, 1, 3, 1, 2, 2, 1, 3, 2, 4, 1, 2, 3, 1, 2, 1, 1, 3, 5, 1, 4, 2, 3, 2, 1, 1, 2, 3, 2, 2, 1, 4, 3, 1, 1, 2, 1, 3, 2, 1, 1, 2, 4, 1, 2, 1, 3, 3, 1, 5, 2, 1, 3, 4, 2, 2, 2, 3, 1, 2, 1, 1, 3, 1, 4, 2, 1, 3, 2, 2, 2, 2, 3, 1, 2
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OFFSET
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1,3
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COMMENTS
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The order of primeness (A078442) of a prime number p is the number of times one must apply A000720 to obtain a nonprime number.
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LINKS
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EXAMPLE
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a(105) = 3 because the prime factor of 105 = 3*5*7 with maximum order of primeness is 5, with order 3.
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MAPLE
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with(numtheory):
p:= proc(n) option remember;
`if`(isprime(n), 1+p(pi(n)), 0)
end:
a:= n-> max(0, map(p, factorset(n))):
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MATHEMATICA
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Table[If[n==1, 0, Max@@(Length[NestWhileList[PrimePi, PrimePi[#], PrimeQ]]&/@FactorInteger[n][[All, 1]])], {n, 100}]
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CROSSREFS
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Cf. A000720, A006450, A007097, A007821, A049076, A076610, A078442, A109082, A114537, A184155, A276625, A279065, A322028, A322030.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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