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A280739 a(n) is the smallest composite number > a(n-1) for which the sum of the prime factors (counted with multiplicity) is n.

%I A280739 #30 Jan 06 2019 19:30:53
%S A280739 4,6,8,10,15,20,21,28,35,56,70,105,140,147,196,198,220,231,260,273,
%T A280739 364,455,459,510,513,570,676,798,1064,1122,1242,1254,1288,1463,1976,
%U A280739 2057,2277,2299,2320,2436,2480,2527,2552,2622,2728,2997,3224,3509,3885,4147,4216,4433,4592,4810,4816,5412,5661,5676,5875,6253
%N A280739 a(n) is the smallest composite number > a(n-1) for which the sum of the prime factors (counted with multiplicity) is n.
%C A280739 Conjecture: a(n) exists for every n >= 4.
%e A280739 For n=11, a(11)=28 because 28 is composite, the factors of 28=2*2*7 are (2,2,7 with multiplicity), and their sum is 11. The composite numbers 40,48,and 54 have the same sum of factors, but we take the smallest > a(10)=21, that is, 28.
%o A280739 (PARI) {
%o A280739 k=4;
%o A280739 for(n=1,10000,
%o A280739     if(!isprime(n),
%o A280739        f=factor(n);
%o A280739        s=sum(i=1, matsize(f)[1], f[i, 1]*f[i, 2]);
%o A280739         if(s==k,
%o A280739            print1(n", ")
%o A280739            ;k++
%o A280739          )
%o A280739       )
%o A280739 )
%o A280739 }
%Y A280739 Cf. A046343
%K A280739 nonn
%O A280739 4,1
%A A280739 _Dimitris Valianatos_, Jan 12 2017