A079094 Arithmetic derivative of (prime(n)+1)*(prime(n+1)+1)/4.

1, 5, 16, 44, 41, 51, 123, 244, 336, 608, 624, 211, 493, 1280, 1836, 1647, 991, 623, 2724, 2256, 2556, 4496, 3483, 2541, 1694, 3896, 7236, 5319, 2122, 12352, 16576, 5925, 5891, 8275, 10180, 6396, 3479, 13780, 13476, 13581, 12993, 26672, 26480

Offset: 1

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A079079, A079093.

Programs

Haskell

a079094 = a003415 . a079079  -- Reinhard Zumkeller, Oct 09 2012

Mathematica

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := ad[(Prime[n]+1) * (Prime[n+1]+1) / 4]; Array[a, 100] (* Amiram Eldar, Apr 06 2025 *)

Formula

a(n) = A003415(A079079(n)).