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A078574 Number of divisors of the average of n-th twin prime pair. 3
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)