OFFSET
1,29
COMMENTS
All terms are powers of 7. Those n such that a(n) > 1 are in A066502.
LINKS
Jianing Song, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(7) = 1, a(7^e) = 7 if e >= 2; for other primes p, a(p^e) = 7 if p == 1 (mod 7), a(p^e) = 1 otherwise.
If the multiplicative group of integers modulo n is isomorphic to C_{k_1} x C_{k_2} x ... x C_{k_m}, where k_i divides k_j for i < j; then a(n) = Product_{i=1..m} gcd(7, k_i).
EXAMPLE
Solutions to x^7 == 1 (mod 29): x == 1, 7, 16, 20, 23, 24, 25 (mod 29).
Solutions to x^7 == 1 (mod 43): x == 1, 4, 11, 16, 21, 35, 41 (mod 43).
Solutions to x^7 == 1 (mod 49): x == 1, 8, 15, 22, 29, 36, 43 (mod 49) (x == 1 (mod 7)).
MATHEMATICA
f[p_, e_] := If[Mod[p, 7] == 1, 7, 1]; f[7, 1] = 1; f[7, e_] := 7; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 10 2023 *)
PROG
(PARI) a(n)=my(Z=znstar(n)[2]); prod(i=1, #Z, gcd(7, Z[i]))
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jianing Song, Sep 10 2018
STATUS
approved