A380827 Least integer k such that the multiplicative group modulo n is a subgroup of the symmetric group S_k.
1, 1, 2, 2, 4, 2, 5, 4, 5, 4, 7, 4, 7, 5, 6, 6, 16, 5, 11, 6, 7, 7, 13, 6, 9, 7, 11, 7, 11, 6, 10, 10, 9, 16, 9, 7, 13, 11, 9, 8, 13, 7, 12, 9, 9, 13, 25, 8, 12, 9, 18, 9, 17, 11, 11, 9, 13, 11, 31, 8, 12, 10, 10, 18, 11, 9, 16, 18, 15, 9, 14, 9, 17, 13, 11, 13, 12, 9, 18, 10, 29
Offset: 1
Keywords
Links
- Asher Gray, Table of n, a(n) for n = 1..10000
- Wikipedia, Multiplicative group of integers modulo n
Formula
a(j*k) = a(j) + a(k) where j and k are coprime and both greater than 2.
a(2j) = j where j is odd.
a(2) = 1, a(4) = 2, a(2^k) = 2 + 2^(k-2) for k >= 3.
a(p^k) = A008475(p-1) * p^(k-1) for odd prime p.