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 A263810 #34 Feb 22 2025 09:57:22
%S A263810 3,4,5,17,257,65537,83623937
%N A263810 Numbers k such that k = tau(k) * phi(k-2) + 1.
%C A263810 Numbers k such that k = A000005(k) * A000010(k-2) + 1.
%C A263810 Sequence deviates from A249541; numbers 4294967297 and 6992962672132097 are not terms of this sequence.
%C A263810 The first 5 known Fermat primes from A019434 are in this sequence.
%C A263810 Conjecture: primes from this sequence are in A254576.
%C A263810 a(8) > 10^25. If k = tau(k) * phi(k-2) + 1 then phi(k-2) must divide k-1, thus k-2 must be a term of A203966, which has already been searched up to 10^25. - _Giovanni Resta_, Feb 21 2020; updated by _Max Alekseyev_, Feb 21 2025
%e A263810 17 is in this sequence because 17 = tau(17)*phi(15) + 1 = 2*8 + 1.
%t A263810 Select[Range@ 100000, # == DivisorSigma[0, #] EulerPhi[# - 2] + 1 &] (* _Michael De Vlieger_, Oct 27 2015 *)
%o A263810 (Magma) [n: n in [3..1000000] | n eq NumberOfDivisors(n) * EulerPhi(n-2) + 1];
%o A263810 (PARI) for(n=3, 1e8, if(numdiv(n)*eulerphi(n-2) == n-1, print1(n ", "))) \\ _Altug Alkan_, Oct 28 2015
%o A263810 (PARI) lista(na, nb) = {my(f1 = factor(na-2), f2 = factor(na-1), f3); for(n=na, nb, f3 = factor(n); if (numdiv(f3)*eulerphi(f1) == n-1, print1(n ", ")); f1 = f2; f2 = f3;);}; \\ _Michel Marcus_, Feb 21 2020
%Y A263810 Cf. A000005, A000010, A019434, A249541, A254576, A203966.
%Y A263810 Cf. A263811 (numbers k such that k = tau(k) * phi(k-1) + 1).
%K A263810 nonn,more
%O A263810 1,1
%A A263810 _Jaroslav Krizek_, Oct 27 2015