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A162989 Lesser of twin primes p such that none of p-1, p+1 and p+3 are cubefree.

%I A162989 #6 Nov 24 2020 16:38:58
%S A162989 69497,416501,474497,632501,960497,1068497,1226501,1402871,1464101,
%T A162989 1635497,1716497,1919429,1986497,2114249,2144501,2283497,2645189,
%U A162989 3120497,3174497,3232751,3305501,3332501,3525497,3637169,3998537
%N A162989 Lesser of twin primes p such that none of p-1, p+1 and p+3 are cubefree.
%H A162989 Robert Israel, <a href="/A162989/b162989.txt">Table of n, a(n) for n = 1..1000</a>
%e A162989 p=69497 and p+2=69499 are twin primes, also:
%e A162989 p-1=69496=2^3*7*17*73
%e A162989 p+1=69498=2*3^5*11*13
%e A162989 p+3=69500=2^2*5^3*139.
%p A162989 cf:= proc(n) local F;
%p A162989     F:= ifactors(n)[2];
%p A162989     max(map(t->t[2],F))>=3
%p A162989 end proc:
%p A162989 select(t -> isprime(t) and isprime(t+2) and cf(t-1) and cf(t+1) and cf(t+3), [seq(i,i=5..10^7,6)]); # _Robert Israel_, Nov 24 2020
%t A162989 f[m_]:=Max[Last/@FactorInteger[m]]>=3;
%t A162989 S={};Do[If[PrimeQ[p=6x-1]&&PrimeQ[p+2]&&
%t A162989 f[p-1]==f[p+1]==f[p+3]==True,AppendTo[S,p]],{x,1,10^6}];S
%Y A162989 Cf. A046099.
%Y A162989 See A162874 for another version.
%K A162989 nonn
%O A162989 1,1
%A A162989 _Zak Seidov_, Jul 19 2009
%E A162989 Definition clarified by _Robert Israel_, Nov 24 2020