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A136177
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Number of exponents in the prime factorization of n that are coprime to n.
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2
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0, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 0, 1, 1, 3, 1, 1, 2, 2, 2, 0, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 0, 2, 3, 1, 1, 2, 3, 1, 0, 1, 2, 2, 1, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 0, 1, 3, 1, 2, 3
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OFFSET
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1,6
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LINKS
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EXAMPLE
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8000 = 2^6 * 5^3. 6 is not coprime to 8000, but 3 is. So a(8000) = 1.
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MATHEMATICA
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Table[Length[Select[Table[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}], GCD[ #, n] == 1 &]], {n, 2, 90}] (* Stefan Steinerberger, Dec 21 2007 *)
Join[{0}, Table[Count[FactorInteger[n][[All, 2]], _?(CoprimeQ[#, n]&)], {n, 2, 110}]] (* Harvey P. Dale, Aug 05 2018 *)
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PROG
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(PARI) A136177(n)={local(t); sum(j=1, #t=factor(n)[, 2]~, gcd(n, t[j])==1)} \\ M. F. Hasler, Dec 21 2007
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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