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

1,2

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.

Formula

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

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

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 *)

Crossrefs

Cf. A000961, A001414, A025473, A025474.

Sequence in context: A071180 A031225 A395051 * A331269 A073907 A131424

Adjacent sequences: A085726 A085727 A085728 * A085730 A085731 A085732

Keyword

nonn

Author

Reinhard Zumkeller, Jul 20 2003

Status

approved