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A046530
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Number of distinct cubic residues mod n.
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18
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1, 2, 3, 3, 5, 6, 3, 5, 3, 10, 11, 9, 5, 6, 15, 10, 17, 6, 7, 15, 9, 22, 23, 15, 21, 10, 7, 9, 29, 30, 11, 19, 33, 34, 15, 9, 13, 14, 15, 25, 41, 18, 15, 33, 15, 46, 47, 30, 15, 42, 51, 15, 53, 14, 55, 15, 21, 58, 59, 45, 21, 22, 9, 37, 25, 66, 23, 51, 69, 30, 71, 15, 25, 26, 63
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Cubic analog of A000224. - S. R. Finch (Steven.Finch(AT)inria.fr), Mar 01 2006
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n (arXiv:math.NT/0604465).
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MAPLE
| A046530 := proc(n)
local a, pf ;
a := 1 ;
if n = 1 then
return 1;
end if;
for i in ifactors(n)[2] do
p := op(1, i) ;
e := op(2, i) ;
if p = 3 then
if e mod 3 = 0 then
a := a*(3^(e+1)+10)/13 ;
elif e mod 3 = 1 then
a := a*(3^(e+1)+30)/13 ;
else
a := a*(3^(e+1)+12)/13 ;
end if;
elif p mod 3 = 2 then
if e mod 3 = 0 then
a := a*(p^(e+2)+p+1)/(p^2+p+1) ;
elif e mod 3 = 1 then
a := a*(p^(e+2)+p^2+p)/(p^2+p+1) ;
else
a := a*(p^(e+2)+p^2+1)/(p^2+p+1) ;
end if;
else
if e mod 3 = 0 then
a := a*(p^(e+2)+2*p^2+3*p+3)/3/(p^2+p+1) ;
elif e mod 3 = 1 then
a := a*(p^(e+2)+3*p^2+3*p+2)/3/(p^2+p+1) ;
else
a := a*(p^(e+2)+3*p^2+2*p+3)/3/(p^2+p+1) ;
end if;
end if;
end do:
a ;
end proc:
seq(A046530(n), n=1..40) ; # R. J. Mathar, Nov 01 2011
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MATHEMATICA
| Length[Union[#]]& /@ Table[Mod[k^3, n], {n, 75}, {k, n}] (* From Jean-François Alcover, Aug 30 2011 *)
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CROSSREFS
| Sequence in context: A053447 A023160 A085312 * A003558 A141419 A072451
Adjacent sequences: A046527 A046528 A046529 * A046531 A046532 A046533
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KEYWORD
| nonn,mult,easy,nice
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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