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 A281622 #23 Jul 26 2025 17:54:45 %S A281622 3,5,17,26,65,4097,65537,262145,1073741825 %N A281622 Numbers k such that sigma(k-1) is a Mersenne prime (A000668). %C A281622 Conjecture 1: the next terms are: 1152921504606846977, 309485009821345068724781057, 81129638414606681695789005144065, 85070591730234615865843651857942052865. %C A281622 Conjecture 2: Union of 26 and A256438. %C A281622 Conjecture 3: Mersenne prime 31 is the only prime p such that p = sigma(x-1) = sigma(y-1) for distinct numbers x and y; 31 = sigma(17-1) = sigma(26-1). %F A281622 Conjecture: a(n) = 2^A090748(n) + 1. - _Daniel Suteu_, Feb 08 2017 %e A281622 65 is a term because sigma(64) = 127 (Mersenne prime). %o A281622 (Magma) [n: n in[2..1000000], k in [1..20] | SumOfDivisors(n-1) eq 2^k-1 and IsPrime(2^k-1)]; %o A281622 (PARI) isok(n) = my(s = sigma(n-1)); isprime(s) && ispower(s+1,,&p) && (p==2); \\ _Michel Marcus_, Jan 27 2017 %Y A281622 Union of 26 and odd terms of A270413. %Y A281622 Prime terms are in A249759. %Y A281622 Subsequence of A270413. %Y A281622 Cf. A000203, A000668, A256438. %K A281622 nonn,more %O A281622 1,1 %A A281622 _Jaroslav Krizek_, Jan 25 2017