A050706 Composites c that reach a prime after 2 iterations of c-> c+sum of prime factors of c.

8, 9, 18, 22, 24, 25, 36, 39, 40, 54, 78, 80, 81, 91, 94, 99, 104, 106, 115, 119, 121, 122, 126, 134, 138, 142, 144, 146, 152, 159, 164, 170, 174, 187, 189, 214, 218, 219, 226, 228, 231, 232, 237, 250, 258, 262, 264, 265, 266, 272, 274, 276, 280, 282, 288, 289

Offset: 1

Author

Patrick De Geest, Aug 15 1999

Keywords

• nonn

Examples

			226 is a term:
Iteration 1: 226 = 2*113 so 226 + (2+113) = 226 + 115 = 341 and composite.
Iteration 2: 341 = 11*31 so 341 + (11+31) = 341 + 42 = 383 and prime.
		

Crossrefs

Cf. A050703, A050704, A050705, A050707, A050708, A050709, A050710.

Programs

Magma

f:=func; a:=[]; for k in [4..300] do if not IsPrime(k) and not IsPrime(f(k)) and IsPrime(f(f(k))) then Append(~a, k); end if; end for; a; // Marius A. Burtea, Oct 18 2019

Mathematica

aQ[n_]:=PrimeQ[Nest[#+Total[Times@@@FactorInteger[#]]&,n,2]]; Select[Range[289],!PrimeQ[#]&&aQ[#]&] (* Jayanta Basu, May 31 2013 *)

Extensions

Name edited by Michel Marcus, Oct 18 2019