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 A351890 #30 Aug 18 2025 18:14:48 %S A351890 5,17,65537,9632244737,20892967937,127831991297,149255504897, %T A351890 159667373057,351108391937,542497063937,1650957730817,2270398022657, %U A351890 2322380932097,2747956028417,2888694547457,3516735087617,6029264167937,6122338640897,6705696695297,11125266727937 %N A351890 Primes p such that tau(p - 1) - 1 = tau(p - 2) = tau(p - 3), where tau(k) is the number of divisors of k (A000005). %C A351890 Corresponding values of tau(a(n)-1): 3, 5, 17, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, ... %C A351890 Corresponding values of tau(a(n)-2) = tau(a(n)-3): 2, 4, 16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, ... %C A351890 Quadruples of [tau(a(n)-3), tau(a(n)-2), tau(a(n)-1), tau(a(n))]: [2, 2, 3, 2], [4, 4, 5, 2], [16, 16, 17, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], ... %C A351890 Quadruple [32, 32, 33, 2] holds for all 128 terms 65537 < a(n) < 10^15. %C A351890 Number p-1 is a perfect square as its number of divisors is odd. %C A351890 The first 3 terms are Fermat primes from A019434. %C A351890 Term 103565955613697 is the smallest primes p such that tau(p - 1) - 1 = tau(p - 2) = tau(p - 3) = tau(p - 4). %e A351890 Quadruple of [tau(65534), tau(65535), tau(65536), tau(65537)]: [16, 16, 17, 2]. %o A351890 (Magma) [m: m in [4..10^6] | IsPrime(m) and #Divisors(m - 1) eq #Divisors(m - 2) + 1 and #Divisors(m - 2) eq #Divisors(m - 3)]; %Y A351890 Subsequence of A347078. %Y A351890 Cf. A000005 (tau), A019434. %K A351890 nonn %O A351890 1,1 %A A351890 _Jaroslav Krizek_, Mar 03 2022