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A185358
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The period of the sequence i^i (mod n) starts from i=a(n).
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2
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1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 1
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OFFSET
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1,8
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LINKS
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FORMULA
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If n = Product_{pi^ei} then a(n) = Max_{1- pi*(1+floor[-ei/pi])}.
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MATHEMATICA
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a[p_, e_]:=1- p*(1+Floor[-e/p]); a[n_]:=Max@Module[{fa=FactorInteger[n]}, Table[a[fa[[i, 1]], fa[[i, 2]]], {i, 1, Length[fa]}]]; Table[a[n], {n, 1, 84}]
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PROG
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(Python)
from sympy import factorint, floor
def a(n):
f=factorint(n)
return 1 if n==1 else max(1 - i*(1 + (-f[i])//i) for i in f)
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CROSSREFS
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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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