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A051265
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Maximal value of prime divisors of numbers in reduced residue system for n.
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5
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0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2
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OFFSET
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1,7
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COMMENTS
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The smallest number for which a(n)=k is the n-th Euclid number (A006862=A002110 + 1).
Largest value of A001221(k) for 1 <= k <= n such that gcd(k, n) = 1. - Michael De Vlieger, Aug 10 2017
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..10000
Z. Abel, E. Demaine, M. Demaine, H. Matsui and G. Rote, Common Developments of Several Different Orthogonal Boxes, CCCG 2011, Toronto ON, August 10-12, 2011.
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FORMULA
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a(n) << log n/log log n. - Charles R Greathouse IV, Aug 10 2017
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EXAMPLE
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For n=60 a(n)=1 since in RRS[ 60 ] only 1 and prime powers occur (see A051250).
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MATHEMATICA
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Table[Max@ Map[PrimeNu, Cases[Range[n - 1], k_ /; CoprimeQ[n, k]]] /. k_ /; ! IntegerQ@ k -> 0, {n, 105}] (* Michael De Vlieger, Aug 10 2017 *)
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PROG
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(PARI) a(n)=my(k=1, s); forprime(p=2, , if(n%p==0, next); k*=p; if(k>n, return(s)); s++) \\ Charles R Greathouse IV, Aug 10 2017
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CROSSREFS
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Records are A006862.
Cf. A001221, A002110, A051250, A051266, A051267, A051268.
Sequence in context: A333145 A335449 A318464 * A008647 A036475 A330746
Adjacent sequences: A051262 A051263 A051264 * A051266 A051267 A051268
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KEYWORD
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nonn,easy
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AUTHOR
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Labos Elemer
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STATUS
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approved
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