A117987 Number of functions f:[n]->[n] such that f[(2*x) mod n]=[2*f(x)] mod n for all x in [n], for n=1,2,3,... Here [n] denotes {0,1,2,...,n-1}.

1, 2, 3, 8, 5, 24, 49, 128, 27, 160, 11, 1536, 13, 6272, 10125, 32768, 289, 13824, 19, 163840, 64827, 22528, 529, 6291456, 125, 106496, 729, 102760448, 29, 331776000, 887503681, 2147483648, 107811, 37879808, 300125, 3623878656, 37, 9961472

Offset: 1

Author

John W. Layman, Apr 11 2006

Keywords

• nonn

Comments

See A117986 and A117988 for results on other modular functional equations.

Crossrefs

Cf. A117986, A117988.

Programs

PARI

{ A117987(n) = my(m,r); m=n\2^valuation(n,2); r=2^(n-m); fordiv(znorder(Mod(2,m)),d, r *= gcd(m,2^d-1)^(sumdiv(d,q, moebius(d\q)*gcd(m,2^q-1) )\d); ); r } /* Max Alekseyev, Jun 11 2009 */

Formula

For n = 2^t * m with odd m, a(n) = 2^(n-m) * \sum_{d|A007733(n)} gcd(m,2^d-1)^{ \sum_{q|d} moebius(d/q) * gcd(m,2^q-1) / d }. - Max Alekseyev, Jun 11 2009

Extensions

Extended by Max Alekseyev, Jun 11 2009