A029912 Start with n; repeatedly sum prime factors (counted with multiplicity) and add 1, until reach 1, 6 or a prime.

1, 3, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 7, 7, 7, 11, 7, 7, 7, 11, 11, 11, 11, 7, 7, 13, 11, 7, 7, 17, 7, 13, 13, 7, 7, 7, 7, 7, 7, 7, 13, 11, 7, 7, 7, 17, 7, 23, 11, 13, 13, 7, 7, 7, 13, 19, 17, 7, 7, 7, 7, 13, 13, 7, 7, 7, 7, 19, 19, 7, 7, 13, 7, 7, 7, 23, 7

Offset: 1

Author

Dann Toliver

Keywords

• nonn

Comments

If p is in A023200 then a(3*p) = p+4. It appears that all n > 35 such that a(n) > n/3 are 3*p for p in A023200. - Robert Israel, Dec 18 2019

Examples

			20 -> 2+2+5+1 = 10 -> 2+5+1 = 8 -> 2+2+2+1 = 7 so a(20)=7.
		

Links

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

Programs

Maple

f:= proc(n) option remember;
  local v;
  v:= add(t[1]*t[2],t=ifactors(n)[2])+1;
  if v = 1 or v = 6 or isprime(v) then return v fi;
  procname(v)
end proc:
map(f, [$1..100]); # Robert Israel, Dec 18 2019

Mathematica

a[n_] := a[n] = If[n==1, 1, Module[{v}, v = Sum[t[[1]]*t[[2]], {t, FactorInteger[n]}]+1; If[v==1 || v==6 || PrimeQ[v], Return[v]]; a[v]]];
a /@ Range[100] (* Jean-François Alcover, Aug 21 2022, after Robert Israel *)