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A052274
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Number of distinct 5th powers mod n.
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14
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1, 2, 3, 3, 5, 6, 7, 5, 7, 10, 3, 9, 13, 14, 15, 9, 17, 14, 19, 15, 21, 6, 23, 15, 5, 26, 19, 21, 29, 30, 7, 17, 9, 34, 35, 21, 37, 38, 39, 25, 9, 42, 43, 9, 35, 46, 47, 27, 43, 10, 51, 39, 53, 38, 15, 35, 57, 58, 59, 45, 13, 14, 49, 34, 65, 18, 67, 51, 69, 70
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OFFSET
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1,2
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COMMENTS
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This sequence is multiplicative. - Leon P Smith, Apr 16 2005
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LINKS
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FORMULA
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Conjecture: a(5^e) = 1+floor[(5-1)*5^(e+3)/(5^5-1)] if e == {0,2,3,4} (mod 5). a(5^e) = 5+floor[(5-1)*5^(e+3)/(5^5-1)] if e==1 (mod 5). - R. J. Mathar, Oct 22 2017
Conjecture: a(p^e) = 1+floor[(p-1)*p^(e+4)/{gcd(p-1,5)*(p^5-1)}] for primes p<>5 - R. J. Mathar, Oct 22 2017
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MAPLE
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{seq( modp(b^5, m), b=0..m-1) };
nops(%) ;
end proc:
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MATHEMATICA
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With[{nn=100}, Table[Length[Union[PowerMod[Range[nn], 5, n]]], {n, nn}]] (* Harvey P. Dale, Mar 19 2016 *)
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PROG
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(PARI) a(n)=my(f=factor(n)); prod(i=1, #f[, 1], my(k=f[i, 1]^f[i, 2]); #vecsort(vector(k, i, i^5%k), , 8)) \\ Charles R Greathouse IV, Sep 05 2013
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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