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

1,1

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A265283 A023836 A064800 * A347299 A230300 A347318

Adjacent sequences: A078571 A078572 A078573 * A078575 A078576 A078577

Keyword

nonn

Author

Reinhard Zumkeller, Nov 29 2002

Status

approved