This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A085014 #22 Mar 27 2021 08:00:21
%S A085014 0,0,0,1,0,1,1,2,1,3,2,1,3,2,2,4,1,2,3,5,4,3,6,4,4,6,4,5,4,6,5,4,2,5,
%T A085014 8,7,5,6,3,3,3,4,5,4,4,5,9,8,7,8,5,8,7,8,4,6,6,7,7,9,6,11,7,8,2,7,12,
%U A085014 8,6,8,4,5,5,6,5,11,10,9,11,5,8,9,12,9,4,7,13,8,5
%N A085014 For p = prime(n), a(n) is the number of primes q such that pq is a base-2 pseudoprime; that is, 2^(pq-1) = 1 mod pq.
%C A085014 Using a construction in Erdős's paper, it can be shown that a(prime(n)) > 0, except for the primes 3, 5, 7 and 13. Using a theorem of Lehmer, it can be shown that the possible values of q are among the prime factors of 2^(p-1)-1. The sequence A085012 gives the smallest prime q such that q*prime(n) is a pseudoprime.
%C A085014 Sequence A086019 gives the largest prime q such that q*prime(n) is a pseudoprime.
%D A085014 Paulo Ribenboim, The New Book of Prime Number Records, Springer, 1996, p. 105-112.
%H A085014 Amiram Eldar, <a href="/A085014/b085014.txt">Table of n, a(n) for n = 2..337</a>
%H A085014 Paul Erdős, <a href="http://www.jstor.org/stable/2304732">On the converse of Fermat's theorem</a>, Amer. Math. Monthly 56 (1949), p. 623-624.
%H A085014 D. H. Lehmer, <a href="http://www.jstor.org/stable/2301798">On the converse of Fermat's theorem</a>, Amer. Math. Monthly 43 (1936), p. 347-354.
%H A085014 <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%F A085014 a(n) < 0.7 * p, where p is the n-th prime. - _Charles R Greathouse IV_, Apr 12 2012
%e A085014 a(11) = 3 because prime(11) = 31 and 2^30-1 has 3 prime factors (11, 151, 331) that yield pseudoprimes when multiplied by 31.
%t A085014 Table[p=Prime[n]; q=Transpose[FactorInteger[2^(p-1)-1]][[1]]; cnt=0; Do[If[PowerMod[2, p*q[[i]]-1, p*q[[i]]]==1, cnt++ ], {i, Length[q]}]; cnt, {n, 2, 50}]
%Y A085014 Cf. A001567 (base-2 pseudoprimes), A085012, A086019, A180471.
%K A085014 nonn
%O A085014 2,8
%A A085014 _T. D. Noe_, Jun 28 2003