

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^(e1) for e >= 1; a(7^e) = 6 for e=1; a(7^e) = 6*7^(e2) for e >= 2; a(p^e) = (p1)*p^(e1) for p == {2,3,4,5,6} (mod 7); a(p^e) = (p1)*p^(e1)/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



