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 A383043 #21 May 01 2025 21:52:20
%S A383043 2,3,4,5,6,7,10,12,13,16,17,18,19,21,28,30,31,36,42,46,54,60,61,63,75,
%T A383043 88,89,99,102,104,106,107,108,126,127,132,133,204,214,216,225,264,270,
%U A383043 286,304,306,324,330,342,352,390,414,420,456,462,468
%N A383043 Integers k such that d*2^k - 1 is prime for some proper divisor d of k.
%e A383043 81 is not in the sequence because 1*2^81 - 1, 3*2^81 - 1, 9*2^81 - 1 and 27*81 - 1 are composites where 1, 3, 9 and 27 are proper divisors d of k = 81, while 81*2^81 - 1 is prime where 81 is nonproper divisor d of k = 81.
%t A383043 s={};Do[d=Drop[Divisors[n],-1];If[ContainsAny[PrimeQ[d*2^n-1],{True}],AppendTo[s,n]],{n,468}];s (* _James C. McMahon_, May 01 2025 *)
%o A383043 (Magma) [k: k in [1..500] | not #[d: d in [1..k-1] | k mod d eq 0 and IsPrime(d*2^k-1)] eq 0];
%o A383043 (PARI) isok(k) = fordiv(k, d, if ((d<k) && ispseudoprime(d*2^k-1), return(1))); \\ _Michel Marcus_, Apr 20 2025
%Y A383043 Supersequence of A000043. Subsequence of A382811.
%Y A383043 Cf. A002234, A032741.
%K A383043 nonn
%O A383043 1,1
%A A383043 _Juri-Stepan Gerasimov_, Apr 19 2025