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 A089200 #27 Aug 26 2024 11:43:24
%S A089200 17,41,73,89,97,109,113,137,163,193,233,241,251,257,271,281,313,337,
%T A089200 353,379,401,409,433,449,457,487,521,541,569,577,593,601,617,641,673,
%U A089200 751,757,761,769,809,811,857,881,919,929,937,953,977
%N A089200 Primes p such that p-1 is divisible by a cube.
%C A089200 This sequence is infinite and its relative density in the sequence of primes is 1 - Product_{p prime} (1-1/(p^2*(p-1))) = 1 - A065414 = 0.30249864150363409671... (Jakimczuk, 2024). - _Amiram Eldar_, Jul 20 2024
%H A089200 Daniel Starodubtsev, <a href="/A089200/b089200.txt">Table of n, a(n) for n = 1..10000</a>
%H A089200 Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.16536.81925">Numbers of the form p-1 where p is prime</a>, ResearchGate preprint, 2024.
%t A089200 f[n_]:=Max[Last/@FactorInteger[n]]; lst={};Do[p=Prime[n];If[f[p-1]>=3,AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 03 2009 *)
%t A089200 Select[Prime[Range[200]],Count[Transpose[FactorInteger[#-1]][[2]], _?(#>2&)]>0&] (* _Harvey P. Dale_, Jan 01 2012 *)
%o A089200 (PARI) ispowerfree(m,p1) = { flag=1; y=component(factor(m),2); for(i=1,length(y), if(y[i] >= p1,flag=0;break); ); return(flag) }
%o A089200 powerfreep3(n,p,k) = { c=0; pc=0; forprime(x=2,n, pc++; if(ispowerfree(x+k,p)==0, c++; print1(x","); ) ); print(); print(c","pc","c/pc+.0) }
%Y A089200 Cf. A039787, A046099, A065414.
%K A089200 easy,nonn
%O A089200 1,1
%A A089200 _Cino Hilliard_, Dec 08 2003