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

1,1

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A171438 A200683 A286541 * A256302 A205396 A082086

Adjacent sequences: A078573 A078574 A078575 * A078577 A078578 A078579

Keyword

nonn

Author

Reinhard Zumkeller, Nov 29 2002

Status

approved