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 A347078 #24 Jul 30 2023 10:54:15
%S A347078 3,5,11,17,197,257,59051,65537,149771,178931,227531,363611,3017171,
%T A347078 4782971,5456897,7935491,10093331,15046643,15896171,20493731,26224643,
%U A347078 27709697,28558337,29986577,51451931,55591937,71014331,72641531,83119691,87441203,98545331,116294657
%N A347078 Primes p such that tau(p - 1) = tau(p - 2) + 1, where tau(k) is the number of divisors of k (A000005).
%C A347078 The first 5 known Fermat primes from A019434 are in the sequence.
%C A347078 Triples of [tau(a(n)-2), tau(a(n)-1), tau(a(n))]: [1, 2, 2], [2, 3, 2], [3, 4, 2], [4, 5, 2], [8, 9, 2], [8, 9, 2], [11, 12, 2], [16, 17, 2], [15, 16, 2], ...
%C A347078 Exactly one of p-1 and p-2 is a perfect square as its number of divisors is odd. - _David A. Corneth_, Sep 05 2021
%H A347078 David A. Corneth, <a href="/A347078/b347078.txt">Table of n, a(n) for n = 1..13040</a> (terms <= 10^15)
%e A347078 Prime 65537 is in the sequence because tau(65536) = tau(65535) + 1 = 16 + 1 = 17.
%t A347078 s = {}; Do[If[PrimeQ[p] && DivisorSigma[0, p - 1] == DivisorSigma[0, p - 2] + 1, AppendTo[s, p]], {p, 3, 5*10^6}]; s (* _Amiram Eldar_, Aug 16 2021 *)
%t A347078 Select[Prime[Range[6650000]],DivisorSigma[0,#-1]==DivisorSigma[0,#-2]+1&] (* _Harvey P. Dale_, Jul 30 2023 *)
%o A347078 (Magma) [m: m in [3..10^7] | IsPrime(m) and #Divisors(m - 1) eq #Divisors(m - 2) + 1]
%o A347078 (PARI) isok(p) = isprime(p) && (numdiv(p-1) == numdiv(p-2)+1); \\ _Michel Marcus_, Aug 16 2021
%Y A347078 Cf. A000005, A019434, A075408.
%K A347078 nonn
%O A347078 1,1
%A A347078 _Jaroslav Krizek_, Aug 15 2021
%E A347078 More terms from _Amiram Eldar_, Aug 16 2021