A081758 Sum of prime factors (with repetition) of sum of prime factors (with repetition) of n.

2, 3, 4, 5, 5, 7, 5, 5, 7, 11, 7, 13, 6, 6, 6, 17, 6, 19, 6, 7, 13, 23, 6, 7, 8, 6, 11, 29, 7, 31, 7, 9, 19, 7, 7, 37, 10, 8, 11, 41, 7, 43, 8, 11, 10, 47, 11, 9, 7, 9, 17, 53, 11, 8, 13, 13, 31, 59, 7, 61, 14, 13, 7, 8, 8, 67, 10, 15, 9, 71, 7, 73, 16, 13, 23, 8, 8, 79, 13, 7, 43, 83, 9, 13, 11

Offset: 2

Author

Reinhard Zumkeller, Apr 08 2003

Keywords

• nonn

Comments

a(n) = A001414(A001414(n)). For further iterations see: A029908, A002217;

a(n)=n iff n is prime or 4.

Examples

			18 = 2*3*3 -> 2+3+3 = 2*2*2 -> 2+2+2 = 6: a(18) = 6.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Programs

Mathematica

spf[n_]:=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]; Table[Nest[Total[spf[#]]&,n,2],{n,2,90}] (* Harvey P. Dale, May 31 2025 *)