A079091 Sum of all prime factors of (prime(n)+1)*(prime(n+1)+1)/4.

3, 5, 7, 9, 12, 13, 13, 14, 15, 16, 27, 29, 23, 22, 18, 19, 41, 50, 29, 47, 48, 23, 23, 25, 34, 37, 28, 27, 38, 34, 28, 42, 40, 27, 36, 102, 122, 57, 46, 45, 33, 33, 110, 114, 31, 69, 70, 39, 52, 47, 33, 36, 37, 61, 64, 32, 37, 162, 189, 123, 90, 37, 40, 177, 213, 141, 111, 60

Offset: 1

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A079079, A079086, A079089, A079090.

Programs

Haskell

a079091 = a001414 . a079079  -- Reinhard Zumkeller, Oct 09 2012

Mathematica

Total[Times@@@FactorInteger[#]]&/@(Times@@(#+1)/4&/@Partition[ Prime[Range[100]],2,1]) (* Harvey P. Dale, May 26 2011 *)

PARI

a(n) = my(f = factor((prime(n)+1)*(prime(n+1)+1)/4)); f[, 1]~ * f[, 2]; \\ Amiram Eldar, Apr 07 2025

Formula

a(n) = A001414(A079079(n)).