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%I #20 Aug 26 2021 14:51:06
%S 69497,69499,416501,416503,474497,474499,632501,632503,960497,960499,
%T 1068497,1068499,1226501,1226503,1402871,1402873,1464101,1464103,
%U 1635497,1635499,1716497,1716499,1919429,1919431,1986497,1986499
%N Twin primes p and r (p < r) such that p-1, p+1 and r+1 are not cubefree.
%C A variant of A162989, which is the main entry. - _N. J. A. Sloane_, Aug 12 2009
%C Note that p+1 = r-1. Thus, the sequence describes twin primes whose immediate neighbors are not cubefree. - _Tanya Khovanova_, Aug 22 2021
%e 69497 and 69499 twin primes. Moreover, 69496 is divisible by 2^3, 69498 is divisible by 3^3, and 69500 is divisible by 5^3. Thus, 69497 and 69499 are in the sequence. - _Tanya Khovanova_, Aug 22 2021
%t s=Select[Prime@Range[200000],PrimeQ[#+2]&&Min[Max[Last/@FactorInteger[#]]&/@{#-1,#+1,#+3}]>2&];Sort@Join[s,s+2] (* _Giorgos Kalogeropoulos_, Aug 22 2021 *)
%o (Python)
%o from sympy import nextprime, factorint
%o def cubefree(n): return max(e for e in factorint(n).values()) <= 2
%o def auptop(limit):
%o alst, p, r = [], 3, 5
%o while p < limit:
%o if r - p == 2 and not any(cubefree(i) for i in [p-1, p+1, r+1]):
%o alst.extend([p, r])
%o p, r = r, nextprime(p)
%o return alst
%o print(auptop(2*10**6)) # _Michael S. Branicky_, Aug 22 2021
%Y Cf. A089189, A089194, A162870, A162872, A162873.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 15 2009
%E Terms corrected by _Zak Seidov_, Jul 19 2009
%E Edited by _N. J. A. Sloane_, Aug 12 2009
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