A280739 - OEIS

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

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OFFSET

4,1

COMMENTS

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

LINKS

Table of n, a(n) for n=4..63.

EXAMPLE

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.

PROG

(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++

)

}