A085729 Sum of prime factors of prime powers.

0, 2, 3, 4, 5, 7, 6, 6, 11, 13, 8, 17, 19, 23, 10, 9, 29, 31, 10, 37, 41, 43, 47, 14, 53, 59, 61, 12, 67, 71, 73, 79, 12, 83, 89, 97, 101, 103, 107, 109, 113, 22, 15, 127, 14, 131, 137, 139, 149, 151, 157, 163, 167, 26, 173, 179, 181, 191, 193, 197, 199, 211, 223

Offset: 1

Author

Reinhard Zumkeller, Jul 20 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Prime Power.
• Eric Weisstein's World of Mathematics, Sum of Prime Factors.

Crossrefs

Cf. A000961, A001414, A025473, A025474.

Programs

Mathematica

s[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 1, Times @@ f[[1]], Nothing]]; s[1] = 0; Array[s, 225] (* Amiram Eldar, May 14 2025 *)

Formula

a(n) = A001414(A000961(n)).

a(n) = e*p when n = p^e: a(n) = A025474(n)*A025473(n).