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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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.

Mathematica

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

Prog

(Magma) f:=func<n|n+(&+[j[1]*j[2]: j in Factorization(n)]) >; 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

Crossrefs

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

Sequence in context: A057104 A359062 A095191 * A159836 A230542 A069809

Adjacent sequences: A050703 A050704 A050705 * A050707 A050708 A050709

Keyword

nonn

Author

Patrick De Geest, Aug 15 1999

Extensions

Name edited by Michel Marcus, Oct 18 2019

Status

approved