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A052275
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Number of distinct 6th powers mod n.
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13
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1, 2, 2, 2, 3, 4, 2, 2, 2, 6, 6, 4, 3, 4, 6, 3, 9, 4, 4, 6, 4, 12, 12, 4, 11, 6, 4, 4, 15, 12, 6, 5, 12, 18, 6, 4, 7, 8, 6, 6, 21, 8, 8, 12, 6, 24, 24, 6, 8, 22, 18, 6, 27, 8, 18, 4, 8, 30, 30, 12, 11, 12, 4, 9, 9, 24, 12, 18, 24, 12, 36, 4, 13, 14, 22, 8, 12, 12
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OFFSET
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1,2
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COMMENTS
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This sequence is multiplicative [Li]. - Leon P Smith, Apr 16 2005
Same as the number of distinct elements that are both squares and cubes mod n. - Steven Finch, Mar 01 2006
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LINKS
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FORMULA
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Conjecture: a(2^n) = 1,2,2,2,3,5,9,18,... with g.f. ( 1-2*x^2-2*x^3-x^4-x^5-2*x^6 ) / ( (x-1)*(2*x-1)*(1+x)*(1+x+x^2)*(x^2-x+1) ). - R. J. Mathar, Sep 28 2017
Conjecture: a(3^n) = 1,2,2,4,10,28,82,.... with g.f. ( 1-x-4*x^2-2*x^3-2*x^4-2*x^5-3*x^6 ) / ( (x-1)*(3*x-1)*(1+x)*(x^2-x+1)*(1+x+x^2) ). - R. J. Mathar, Sep 28 2017
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MAPLE
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{seq( modp(b^6, m), b=0..m-1) };
nops(%) ;
end proc:
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MATHEMATICA
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Length[Union[#]]&/@Table[PowerMod[k, 6, n], {n, 100}, {k, n}] (* Zak Seidov, Feb 17 2013 *)
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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^6%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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