A118701 Largest prime power that divides the average of twin-prime pairs.

4, 3, 4, 9, 5, 7, 5, 9, 17, 27, 23, 25, 9, 64, 11, 19, 16, 27, 47, 13, 29, 7, 27, 11, 29, 19, 25, 103, 107, 11, 81, 137, 23, 13, 49, 17, 43, 25, 59, 13, 128, 41, 71, 43, 31, 11, 17, 121, 19, 31, 67, 81, 139, 283, 41, 149, 16, 313, 23, 25, 37, 169, 347, 29, 64

Offset: 1

Author

Greg Huber, Jul 13 2006

Keywords

• nonn

Examples

			a(10) = 27 since the 10th twin-prime pair is (107, 109) and 108 = 4*27.
		

Links

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

Crossrefs

Cf. A014574, A034699, A060210, A246655.

Programs

Mathematica

Max[Power @@@ FactorInteger[#]] & /@ (Select[Prime[Range[350]], PrimeQ[# + 2] &] + 1) (* Amiram Eldar, May 25 2024 *)

PARI

maxpow(n) = {my(f = factor(n)); if(n == 1, 1, vecmax(vector(#f~, i, f[i,1]^f[i,2])));}
lista(pmax) = {my(prev = 2); forprime(p = 3, pmax, if(p == prev + 2, print1(maxpow(p - 1), ", ")); prev = p);} \\ Amiram Eldar, May 25 2024

Formula

a(n) = A034699(A014574(n)). - Amiram Eldar, May 25 2024

Extensions

More terms from Amiram Eldar, May 25 2024