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A293484 The number of 7th powers in the multiplicative group modulo n. 2
1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 4, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 6, 20, 24, 22, 46, 16, 6, 20, 32, 24, 52, 18, 40, 24, 36, 4, 58, 16, 60, 30, 36, 32, 48, 20, 66, 32, 44, 24, 10, 24, 72, 36, 40, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The size of the set of numbers j^7 mod n, gcd(j,n)=1, 1 <= j <= n.

A000010(n) / a(n) is another multiplicative integer sequence (size of the kernel of the isomorphism of the multiplicative group modulo n to the multiplicative group of 7th powers modulo n).

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..10116

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 <= 1; a(2^e) = 2^(e-1) for e >= 1; a(7^e) = 6 for e=1; a(7^e) = 6*7^(e-2) for e >= 2; a(p^e) = (p-1)*p^(e-1) for p == {2,3,4,5,6} (mod 7); a(p^e) = (p-1)*p^(e-1)/7 for p == 1 (mod 7). - R. J. Mathar, Oct 13 2017

MAPLE

A293484 := proc(n)

    local r, j;

    r := {} ;

    for j from 1 to n do

        if igcd(j, n)= 1 then

            r := r union { modp(j &^ 7, n) } ;

        end if;

    end do:

    nops(r) ;

end proc:

seq(A293484(n), n=1..120) ;

CROSSREFS

Cf. A046073 (2nd), A087692 (3rd), A250207 (4th), A293482, A293483, A293485, A085310.

Sequence in context: A011773 A080737 A152455 * A000010 A003978 A122645

Adjacent sequences:  A293481 A293482 A293483 * A293485 A293486 A293487

KEYWORD

nonn,mult

AUTHOR

R. J. Mathar, Oct 10 2017

STATUS

approved

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Last modified August 21 18:08 EDT 2018. Contains 313955 sequences. (Running on oeis4.)