A078573 Maximal exponent in prime factorization of the average of n-th twin prime pair.

2, 1, 2, 2, 1, 1, 2, 3, 1, 3, 1, 2, 2, 6, 2, 2, 4, 3, 1, 3, 2, 2, 4, 1, 2, 1, 3, 1, 1, 2, 4, 1, 2, 1, 2, 2, 3, 2, 2, 2, 7, 1, 2, 1, 1, 3, 2, 2, 1, 4, 3, 4, 2, 1, 1, 2, 4, 1, 2, 2, 3, 2, 1, 3, 6, 1, 2, 1, 4, 1, 2, 1, 2, 5, 1, 7, 3, 1, 2, 1, 3, 3, 4, 5, 2, 2, 2, 2, 5, 2, 1, 1, 2, 3, 2, 1, 2, 3, 3, 2, 2, 1, 1, 1, 2

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A051903(A014574(n)).

Example

10th twin prime pair = (A001359(10), A006512(10)) = (107,109), hence A014574(10) = 108 = 2^2 * 3^2, therefore a(10) = 3.

Mathematica

midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; f[n_] := Max @@ FactorInteger[n][[;; , 2]]; f /@ Select[Range[5000], midQ] (* Amiram Eldar, Nov 03 2019 *)
Max[FactorInteger[Mean[#]][[All, 2]]]&/@Select[Partition[Prime[Range[1000]], 2, 1], #[[2]] - #[[1]]==2&] (* Harvey P. Dale, Apr 21 2022 *)

Crossrefs

Cf. A051903, A014574, A078570, A078572.

Sequence in context: A095955 A272772 A293431 * A143786 A232353 A366987

Adjacent sequences: A078570 A078571 A078572 * A078574 A078575 A078576

Keyword

nonn

Author

Reinhard Zumkeller, Nov 29 2002

Status

approved