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%I #35 Sep 19 2024 14:41:53
%S 4,6,8,9,10,12,16,18,20,22,24,25,27,32,34,36,40,44,48,49,50,54,58,64,
%T 68,72,80,81,82,88,96,100,108,116,118,121,125,128,136,142,144,160,162,
%U 164,165,169,176,192,200,202,210,214,216,232,236,242,243,250,256,272
%N Composite numbers that become prime after exactly 1 iteration of f(k) = sum of distinct prime factors of k.
%C f(k) = sum of prime factors without multiplicity, so that f(1500) = 2+3+5 = 10.
%C The sequence is infinite because f(2^m * 5^s) = 2 + 5 = 7, for m,s >= 1. - _Marius A. Burtea_, Jan 21 2019
%H Marius A. Burtea, <a href="/A047820/b047820.txt">Table of n, a(n) for n = 1..10122</a>
%t Select[ Range@280, (fi = FactorInteger@#; Plus @@ Last /@ fi > 1 && PrimeQ[Plus @@ First /@ fi]) &] (* _Robert G. Wilson v_, Dec 09 2005 *)
%t Select[Range[300],CompositeQ[#]&&PrimeQ[Total[FactorInteger[#][[;;,1]]]]&] (* _Harvey P. Dale_, Sep 18 2024 *)
%o (Magma) [n:n in [1..300]| IsPrime(&+PrimeDivisors(n)) and not IsPrime(n)]; // _Marius A. Burtea_, Jan 21 2019
%o (PARI) is(n) = isprime(vecsum(factor(n)[, 1])) && !isprime(n) \\ _David A. Corneth_, Jan 21 2019
%Y Cf. A000040, A002808, A008472.
%K nonn
%O 1,1
%A _David W. Wilson_