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 A278741 #21 Jul 20 2025 15:03:59
%S A278741 3,5,17,65,1025,4097,65537,262145,4194305,268435457,1073741825,
%T A278741 68719476737,1099511627777,4398046511105,70368744177665,
%U A278741 4503599627370497,288230376151711745,1152921504606846977,73786976294838206465,1180591620717411303425,4722366482869645213697
%N A278741 Odd numbers k such that tau(k-1) is a prime.
%C A278741 tau(k) = A000005(k) = the number of divisors of k.
%C A278741 Conjecture: prime terms are in A249759: 3, 5, 17, 65537, ...
%C A278741 Supersequence of A256438 and A249759. Subsequence of {A009087(n) + 1}.
%F A278741 a(n) = A061286(n) + 1.
%F A278741 sigma(a(n)-1) = A001348(n), i.e., Mersenne numbers.
%F A278741 tau(a(n)-1) = A000040(n), i.e., all primes; a(n) = the smallest odd number k such that tau(a(n)-1) = prime(n) = A000040(n).
%e A278741 Odd number 65 is in the sequence because tau(64) = 7 (prime).
%o A278741 (Magma) [n: n in[2..10000000] | IsOdd(n) and IsPrime(NumberOfDivisors(n-1))];
%o A278741 (PARI) isok(n) = (n % 2) && isprime(numdiv(n-1)); \\ _Michel Marcus_, Nov 27 2016
%Y A278741 Cf. A000005, A000040, A001348, A009087, A061286, A249759, A256438.
%K A278741 nonn
%O A278741 1,1
%A A278741 _Jaroslav Krizek_, Nov 27 2016