

A078574


Number of divisors of the average of nth 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
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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?, BitPlayer 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[n1] && 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



