A078576 Sum of distinct prime factors of the average of n-th twin prime pair.

2, 5, 5, 5, 10, 12, 10, 5, 22, 5, 28, 10, 10, 5, 16, 24, 10, 10, 52, 18, 34, 17, 5, 23, 34, 29, 10, 108, 112, 21, 10, 142, 28, 29, 12, 27, 48, 17, 64, 25, 5, 51, 76, 53, 43, 21, 29, 16, 37, 36, 72, 10, 144, 288, 53, 154, 18, 318, 35, 23, 42, 18, 352, 34, 16, 81, 29, 378, 12

Offset: 1

Author

Reinhard Zumkeller, Nov 29 2002

Keywords

• nonn

Examples

			12th twin prime pair = (A001359(12), A006512(12)) = (149,151), hence A014574(12) = 150 = 2*3*5*5, therefore a(12) = 2+3+5 = 10.
		

Links

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

Crossrefs

Cf. A008472, A014574, A078577, A078575, A078570.

Programs

Mathematica

midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; f[n_] := Plus @@ FactorInteger[n][[;;,1]]; f /@ Select[Range[3000], midQ] (* Amiram Eldar, Nov 03 2019 *)
Total[FactorInteger[#][[;;,1]]]&/@Mean/@Select[Partition[Prime[Range[350]],2,1],#[[2]]-#[[1]]==2&] (* Harvey P. Dale, Jan 21 2025 *)

Formula

a(n) = A008472(A014574(n)).