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Number of divisors of the average of n-th twin prime pair.
3

%I #17 Nov 07 2022 15:40:28

%S 3,4,6,6,8,8,12,12,8,12,8,12,18,14,12,12,20,16,8,16,12,24,20,16,12,16,

%T 24,8,8,24,20,8,18,16,18,24,16,24,12,24,24,16,12,16,16,32,24,18,16,20,

%U 16,30,12,8,16,12,30,8,24,24,16,18,8,24,28,16,24,8,30,32,36,8,24,30,8

%N Number of divisors of the average of n-th twin prime pair.

%H Amiram Eldar, <a href="/A078574/b078574.txt">Table of n, a(n) for n = 1..10000</a>

%H Brian Hayes, <a href="http://bit-player.org/2021/does-having-prime-neighbors-make-you-more-composite">Does having prime neighbors make you more composite?</a>, Bit-Player Article, Nov 04 2021

%F a(n) = A000005(A014574(n)).

%e 4th twin prime pair = (A001359(4), A006512(4)) = (17,19), hence A014574(4) = 18 with divisors = {1,2,3,6,9,18} therefore a(4) = 6.

%t midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; DivisorSigma[0, Select[Range[3000], midQ]] (* _Amiram Eldar_, Nov 03 2019 *)

%t DivisorSigma[0,#]&/@(Mean/@Select[Partition[Prime[Range[500]],2,1],#[[2]]- #[[1]] == 2&]) (* _Harvey P. Dale_, Nov 07 2022 *)

%Y Cf. A000005, A014574, A078570, A078571, A078575.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Nov 29 2002