A086256 Number of base-2 Fermat pseudoprimes that divide 2^n-1.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 4, 1, 2, 1, 1, 0, 13, 4, 5, 0, 2, 2, 1, 1, 13, 1, 1, 4, 7, 1, 11, 4, 14, 9, 4, 4, 28, 0, 12, 11, 12, 4, 2, 5, 28, 4, 26, 1, 63, 0, 1, 5, 12, 1, 29, 1, 12, 2, 44, 4, 101, 4, 11, 27, 12, 1, 26, 4, 15, 4, 11, 1, 75, 1, 11, 14, 36, 0, 40, 11

Offset: 1

Author

T. D. Noe, Jul 14 2003

Keywords

• nonn
• hard

Comments

A base-2 Fermat pseudoprime is a composite number x such that 2^x = 2 mod x.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..419
• Eric Weisstein's World of Mathematics, Pseudoprime

Crossrefs

Cf. A001567 (base-2 pseudoprimes), A046801, A086249.

Programs

Mathematica

Table[d=Divisors[2^n-1]; cnt=0; Do[m=d[[i]]; If[ !PrimeQ[m]&&PowerMod[2, m, m]==2, cnt++ ], {i, Length[d]}]; cnt, {n, 100}]

Formula

a(n) = Sum{d|n} A086249(d), the Mobius transform of A086249.