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

4, 6, 8, 10, 15, 20, 21, 28, 35, 56, 70, 105, 140, 147, 196, 198, 220, 231, 260, 273, 364, 455, 459, 510, 513, 570, 676, 798, 1064, 1122, 1242, 1254, 1288, 1463, 1976, 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

Offset: 4

Author

Dimitris Valianatos, Jan 12 2017

Keywords

• nonn

Comments

Conjecture: a(n) exists for every n >= 4.

Examples

			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.
		

Crossrefs

Cf. A046343

Programs

PARI

{
k=4;
for(n=1,10000,
    if(!isprime(n),
       f=factor(n);
       s=sum(i=1, matsize(f)[1], f[i, 1]*f[i, 2]);
        if(s==k,
           print1(n", ")
           ;k++
         )
      )
)
}