[seqfan] Rule needed

[Artur]

Dear Seqfans,
I need help with finding rule on follwing problem
Sequences:
B={1, 3, 7, 15, 27, 63, 125, 243, 343, 999, 1805, 3721, 8181, 16335, 
32761, 65533, 112847, 190269, 519375, 1046875, 1953125}
C={2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 
32768, 65536, 131072, 262144, 524288, 1048576, 2097152}
A={1, 1, 1, 1, 5, 1, 3, 13, 169, 25, 243, 375, 11, 49, 7, 3, 18225, 
71875, 4913, 1701, 144027}
C(n) = 2^n
A(n) = C(n) - B(n)
A(n) < B(n) < C(n)
is obtained by algorhitm such
that GCD[A(n),B(n),C(n)] = 1 and product of distinct prime divisors of 
A(n)*B(n)*C(n) have minimal value.
I'm looking for formula for B(n).
Who can help?
Best wishes
Artur