A078573 The maximum 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

Author

Reinhard Zumkeller, Nov 29 2002

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A001359, A006512, A051903, A014574, A078570, A078572.

Programs

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 *)

PARI

lista(pmax) = {my(prv = 2); forprime(p = 3, pmax, if(p - prv ==2, print1(vecmax(factor(p-1)[,2]), ", ")); prv = p);} \\ Amiram Eldar, Sep 09 2024

Formula

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