A078574 Number of divisors of the average of n-th twin prime pair.

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

Offset: 1

Author

Reinhard Zumkeller, Nov 29 2002

Keywords

• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Brian Hayes, Does having prime neighbors make you more composite?, Bit-Player Article, Nov 04 2021

Crossrefs

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

Programs

Mathematica

midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; DivisorSigma[0, Select[Range[3000], midQ]] (* Amiram Eldar, Nov 03 2019 *)
DivisorSigma[0,#]&/@(Mean/@Select[Partition[Prime[Range[500]],2,1],#[[2]]- #[[1]] == 2&]) (* Harvey P. Dale, Nov 07 2022 *)

Formula

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