A211455 The number of bases b for which A181780(n) is a Fermat pseudoprime.

2, 2, 2, 2, 2, 2, 2, 6, 4, 2, 2, 2, 2, 2, 14, 4, 2, 2, 2, 2, 2, 14, 2, 34, 2, 2, 2, 14, 2, 2, 2, 6, 2, 8, 2, 2, 2, 2, 2, 34, 2, 2, 2, 14, 2, 2, 14, 2, 2, 2, 2, 14, 10, 2, 2, 10, 4, 2, 2, 14, 4, 2, 2, 8, 6, 2, 2, 2, 14, 2, 2, 2, 2, 2, 34, 2, 14, 6, 38, 6, 2, 2

Offset: 1

Author

T. D. Noe, Apr 13 2012

Keywords

• nonn

Comments

Sequences A211456 and A211457 give the smallest and largest bases b; A211458 lists all bases.

Every term in this sequence is even. - Geoffrey Critzer, Apr 08 2015

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A181780, A211456, A211457, A211458.

Programs

Mathematica

t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n], s = Select[Range[2, n-2], PowerMod[#, n-1, n] == 1 &]; If[s != {}, AppendTo[t, {n, Length[s], s}]]]]; Transpose[t][[2]]
f[n_] := If[ PrimeQ@ n, {}, Count[ Table[ PowerMod[k, n - 1, n], {k, 2, n - 2}], 1]] /. {0 -> {}}; Array[f, 237] // Flatten (* Robert G. Wilson v, Apr 08 2015 *)

Formula

a(n) = A063994(m) - 2 for odd m in A181780. a(n) = A063994(m) - 1 for even m in A181780. - Thomas Ordowski, Dec 13 2013