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%I #6 Sep 09 2015 19:47:30
%S 1,2,3,8,5,24,49,128,27,160,11,1536,13,6272,10125,32768,289,13824,19,
%T 163840,64827,22528,529,6291456,125,106496,729,102760448,29,331776000,
%U 887503681,2147483648,107811,37879808,300125,3623878656,37,9961472
%N 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}.
%C See A117986 and A117988 for results on other modular functional equations.
%F 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
%o (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 */
%Y Cf. A117986, A117988.
%K nonn
%O 1,2
%A _John W. Layman_, Apr 11 2006
%E Extended by _Max Alekseyev_, Jun 11 2009
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