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A118701 Largest prime power that divides the average of twin-prime pairs.

%I A118701 #11 May 25 2024 04:23:21
%S A118701 4,3,4,9,5,7,5,9,17,27,23,25,9,64,11,19,16,27,47,13,29,7,27,11,29,19,
%T A118701 25,103,107,11,81,137,23,13,49,17,43,25,59,13,128,41,71,43,31,11,17,
%U A118701 121,19,31,67,81,139,283,41,149,16,313,23,25,37,169,347,29,64
%N A118701 Largest prime power that divides the average of twin-prime pairs.
%H A118701 Amiram Eldar, <a href="/A118701/b118701.txt">Table of n, a(n) for n = 1..10000</a>
%F A118701 a(n) = A034699(A014574(n)). - _Amiram Eldar_, May 25 2024
%e A118701 a(10) = 27 since the 10th twin-prime pair is (107, 109) and 108 = 4*27.
%t A118701 Max[Power @@@ FactorInteger[#]] & /@ (Select[Prime[Range[350]], PrimeQ[# + 2] &] + 1) (* _Amiram Eldar_, May 25 2024 *)
%o A118701 (PARI) maxpow(n) = {my(f = factor(n)); if(n == 1, 1, vecmax(vector(#f~, i, f[i,1]^f[i,2])));}
%o A118701 lista(pmax) = {my(prev = 2); forprime(p = 3, pmax, if(p == prev + 2, print1(maxpow(p - 1), ", ")); prev = p);} \\ _Amiram Eldar_, May 25 2024
%Y A118701 Cf. A014574, A034699, A060210, A246655.
%K A118701 nonn
%O A118701 1,1
%A A118701 _Greg Huber_, Jul 13 2006
%E A118701 More terms from _Amiram Eldar_, May 25 2024