OFFSET
1,2
COMMENTS
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
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).
S. Li, On the number of elements with maximal order in the multiplicative group modulo n, Acta Arithm. 86 (2) (1998) 113, see proof of theorem 2.1
FORMULA
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
MAPLE
A052275 := proc(m)
{seq( modp(b^6, m), b=0..m-1) };
nops(%) ;
end proc:
seq(A052275(m), m=1..100) ; # R. J. Mathar, Sep 22 2017
MATHEMATICA
Length[Union[#]]&/@Table[PowerMod[k, 6, n], {n, 100}, {k, n}] (* Zak Seidov, Feb 17 2013 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
N. J. A. Sloane, Feb 05 2000
STATUS
approved