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 A089189 #35 Feb 16 2021 04:32:30
%S A089189 2,3,5,7,11,13,19,23,29,31,37,43,47,53,59,61,67,71,79,83,101,103,107,
%T A089189 127,131,139,149,151,157,167,173,179,181,191,197,199,211,223,227,229,
%U A089189 239,263,269,277,283,293,307,311,317,331,347,349,359,367,373,383
%N A089189 Primes p such that p-1 is cubefree.
%C A089189 The ratio of the count of primes p <= n such that p-1 is cubefree to the count of primes <= n converges to 0.69.. . This implies that roughly 70% of the primes less one are cubefree. This compares to about 0.37 of the primes less one are squarefree.
%C A089189 More accurately, the density of this sequence within the primes is Product_{p prime} (1-1/(p^2*(p-1))) = 0.697501... (A065414) (Mirsky, 1949). - _Amiram Eldar_, Feb 16 2021
%H A089189 Reinhard Zumkeller and Vincenzo Librandi, <a href="/A089189/b089189.txt">Table of n, a(n) for n = 1..10000</a>
%H A089189 Leon Mirsky, <a href="http://www.jstor.org/stable/2305811">The number of representations of an integer as the sum of a prime and a k-free integer</a>, American Mathematial Monthly 56:1 (1949), pp. 17-19.
%F A089189 A212793(a(n) - 1) = 1. - _Reinhard Zumkeller_, May 27 2012
%e A089189 43 is included because 43-1 = 2*3*7.
%e A089189 41 is omitted because 41-1 = 2^3*5.
%e A089189 97 is omitted because 96 = 2^5*3 since higher powers are also tested for exclusion.
%p A089189 filter:= p -> isprime(p) and max(seq(t[2],t=ifactors(p-1)[2]))<=2:
%p A089189 select(filter, [2,seq(2*i+1,i=1..1000)]); # _Robert Israel_, Sep 11 2014
%t A089189 f[n_]:=Module[{a=m=0},Do[If[FactorInteger[n][[m,2]]>2,a=1],{m,Length[FactorInteger[n]]}];a]; lst={};Do[p=Prime[n];If[f[p-1]==0,AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 15 2009 *)
%t A089189 Select[Prime[Range[100]],Max[Transpose[FactorInteger[#-1]][[2]]]<3&] (* _Harvey P. Dale_, Feb 05 2012 *)
%o A089189 (Haskell)
%o A089189 a097375 n = a097375_list !! (n-1)
%o A089189 a097375_list = filter ((== 1) . a212793 . (subtract 1)) a000040_list
%o A089189 -- _Reinhard Zumkeller_, May 27 2012
%o A089189 (PARI) lista(nn) = forprime(p=2, nn, f = factor(p-1)[,2]; if ((#f == 0) || vecmax(f) < 3, print1(p, ", "));) \\ _Michel Marcus_, Sep 11 2014
%Y A089189 Cf. A004709, A039787, A065414, A097380, A089194 (subsequence).
%K A089189 easy,nonn
%O A089189 1,1
%A A089189 _Cino Hilliard_, Dec 08 2003 and _Reinhard Zumkeller_, Aug 11 2004
%E A089189 Corrected and extended by _Harvey P. Dale_, Feb 05 2012