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A293483 The number of 6th powers in the multiplicative group modulo n. 5
1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 5, 1, 2, 1, 2, 2, 8, 1, 3, 2, 1, 5, 11, 1, 10, 2, 3, 1, 14, 2, 5, 4, 5, 8, 2, 1, 6, 3, 2, 2, 20, 1, 7, 5, 2, 11, 23, 2, 7, 10, 8, 2, 26, 3, 10, 1, 3, 14, 29, 2, 10, 5, 1, 8, 4, 5, 11, 8, 11, 2, 35, 1, 12, 6, 10, 3, 5, 2, 13, 4, 9, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The size of the set of numbers j^6 mod n, gcd(j,n)=1, 1 <= j <= n.

A000010(n) / a(n) is another multiplicative integer sequence.

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..10132

Richard J. Mathar, Size of the Set of Residues of Integer Powers of Fixed Exponent, research paper, 2017.

FORMULA

Conjecture: a(2^e) = 1 for e <= 3; a(2^e) = 2^(e-3) for e >= 3; a(3^e) = 1 for e <= 2; a(3^e) = 3^(e-2) for e >= 2; a(p^e) = (p-1)*p^(e-1)/2 for p == 5 (mod 6); a(p^e) = (p-1)*p^(e-1)/6 for p == 1 (mod 6). - R. J. Mathar, Oct 13 2017

a(n) = A000010(n)/A319100(n). This implies that the conjecture above is true. - Jianing Song, Nov 10 2019

MAPLE

A293483 := proc(n)

    local r, j;

    r := {} ;

    for j from 1 to n do

        if igcd(j, n)= 1 then

            r := r union { modp(j &^ 6, n) } ;

        end if;

    end do:

    nops(r) ;

end proc:

seq(A293483(n), n=1..120) ;

CROSSREFS

The number of k-th powers in the multiplicative group modulo n: A046073 (k=2), A087692 (k=3), A250207 (k=4), A293482 (k=5), this sequence (k=6), A293484 (k=7), A293485 (k=8).

Cf. A052275, A319100, A000010.

Sequence in context: A106498 A093466 A257463 * A125761 A154950 A260089

Adjacent sequences:  A293480 A293481 A293482 * A293484 A293485 A293486

KEYWORD

nonn,mult,changed

AUTHOR

R. J. Mathar, Oct 10 2017

STATUS

approved

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Last modified November 15 08:55 EST 2019. Contains 329144 sequences. (Running on oeis4.)