A053477 Sum of iterates of divisor number function A000005.

1, 2, 5, 9, 7, 15, 9, 17, 14, 19, 13, 27, 15, 23, 24, 23, 19, 33, 21, 35, 30, 31, 25, 41, 30, 35, 36, 43, 31, 47, 33, 47, 42, 43, 44, 50, 39, 47, 48, 57, 43, 59, 45, 59, 60, 55, 49, 67, 54, 65, 60, 67, 55, 71, 64, 73, 66, 67, 61, 87, 63, 71, 78, 73, 74, 83, 69, 83, 78, 87, 73

Offset: 1

Author

Labos Elemer, Jan 14 2000

Keywords

• nonn

Examples

			If n is prime then the iteration sequence is {p,2} and the sum is p+2. If n=30, then iterations of the d function are {30,8,4,3,2} and their sum is a(30)=47.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A036452, A036453, A036454, A036455, A036459.

Programs

Maple

f:= proc(n) option remember;
  if n <= 2 then n
  else n + procname(numtheory:-tau(n));
  fi
end proc:
map(f, [$1..80]); # Robert Israel, Nov 14 2016

Mathematica

g[n_] := DivisorSigma[0, n]; f[n_] := Plus @@ Drop[ FixedPointList[g, n], -1]; Table[ f[n], {n, 71}] (* Robert G. Wilson v, Dec 16 2004 *)