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Composites c that reach a prime after 2 iterations of c-> c+sum of prime factors of c.
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%I #19 Sep 08 2022 08:44:58

%S 8,9,18,22,24,25,36,39,40,54,78,80,81,91,94,99,104,106,115,119,121,

%T 122,126,134,138,142,144,146,152,159,164,170,174,187,189,214,218,219,

%U 226,228,231,232,237,250,258,262,264,265,266,272,274,276,280,282,288,289

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

%e 226 is a term:

%e Iteration 1: 226 = 2*113 so 226 + (2+113) = 226 + 115 = 341 and composite.

%e Iteration 2: 341 = 11*31 so 341 + (11+31) = 341 + 42 = 383 and prime.

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

%o (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

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

%K nonn

%O 1,1

%A _Patrick De Geest_, Aug 15 1999

%E Name edited by _Michel Marcus_, Oct 18 2019