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 A332740 #10 Feb 23 2020 02:25:12 %S A332740 229,8293,9829,14887,16087,20389,21493,44983,50581,53887,57943,63463, %T A332740 64663,72223,81547,93253,108343,134917,138727,143239,157207,192613, %U A332740 199669,203653,206407,210853,218839,244837,248749,251287,255049,262693,280183,296437,300319 %N A332740 Prime numbers p such that the set of composite numbers in the range [p+1, nextprime(p)-1] has more than one element and all the elements have the same number of divisors. %C A332740 The corresponding numbers of divisors are 8, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 24, 24, ... and the number of divisors in the order of their first appearance are 8, 16, 24, 20, 12, 32, 48, ... %C A332740 The number of composites between a(n) and its next prime are 3, 3, 3, 3, 3, 3, 5, 3, 5, 3, ... Are there terms with number of composites larger than 5? %H A332740 Amiram Eldar, <a href="/A332740/b332740.txt">Table of n, a(n) for n = 1..10000</a> %e A332740 229 is a term since between 229 and its next prime, 233, there are 3 composite numbers, 230, 231 and 232 and all of them have the same number of divisors, 8. %t A332740 seqQ[n_] := PrimeQ[n] && (nx=NextPrime[n]) > n + 2 && Length @ Union @ DivisorSigma[0, Range[n+1, nx-1]] == 1; Select[Range[10^6], seqQ] %Y A332740 Cf. A000005, A075580, A075583, A075584, A075585, A075586, A075587, A075588, A075589. %K A332740 nonn %O A332740 1,1 %A A332740 _Amiram Eldar_, Feb 21 2020