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A087713 Greatest prime factor of the product of the neighbors of the n-th prime.

%I A087713 #32 Apr 16 2025 21:33:43
%S A087713 3,2,3,3,5,7,3,5,11,7,5,19,7,11,23,13,29,31,17,7,37,13,41,11,7,17,17,
%T A087713 53,11,19,7,13,23,23,37,19,79,41,83,43,89,13,19,97,11,11,53,37,113,23,
%U A087713 29,17,11,7,43,131,67,17,139,47,71,73,17,31,157,79,83,13,173,29,59
%N A087713 Greatest prime factor of the product of the neighbors of the n-th prime.
%C A087713 Apparently a(n) = A024710(n) for n>4. - _Georg Fischer_, Oct 06 2018
%C A087713 Conjecture: The record values are A120628 \ {2}. - _Jason Yuen_, Jan 19 2025
%H A087713 Reinhard Zumkeller, <a href="/A087713/b087713.txt">Table of n, a(n) for n = 1..10000</a>
%H A087713 Davide Rotondo and others, <a href="https://groups.google.com/g/seqfan/c/CHfoEXqnnjA">A120628 and record numbers of a087713</a>, Conversation in the SeqFan Google Group, Dec 25 2024.
%F A087713 a(n) = A006530((A000040(n)-1)*(A000040(n)+1)) = A006530(A006093(n)*A008864(n)) = A006530(A084920(n)).
%F A087713 a(n) <= (prime(n)+1)/2, n > 1. - _Ya-Ping Lu_, Apr 10 2025
%e A087713 a(10) = A006530(prime(10)^2 - 1) = A006530(29*29-1) = A006530(840) = A006530(7*5*3*2^3) = 7.
%t A087713 FactorInteger[#][[-1,1]]&/@((#-1)(#+1)&/@Prime[Range[80]]) (* _Harvey P. Dale_, Oct 26 2019 *)
%o A087713 (Haskell)
%o A087713 a087713 = a006530 . a084920  -- _Reinhard Zumkeller_, Aug 27 2013
%o A087713 (PARI) a(n) = my(p=prime(n)); vecmax(factor((p-1)*(p+1))[, 1]); \\ _Michel Marcus_, Jan 20 2025
%o A087713 (Python)
%o A087713 from sympy import prime, primefactors
%o A087713 def A087713(n): p = prime(n); return max(primefactors(p*p-1))  # _Ya-Ping Lu_, Mar 07 2025
%Y A087713 Cf. A006530, A084920, A120628.
%K A087713 nonn,easy
%O A087713 1,1
%A A087713 _Reinhard Zumkeller_, Sep 28 2003
%E A087713 Definition clarified by _Harvey P. Dale_, Oct 26 2019