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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.
1
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
4,1
COMMENTS
Conjecture: a(n) exists for every n >= 4.
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++
)
)
)
}
CROSSREFS
Sequence in context: A127792 A288814 A062711 * A353917 A117347 A088011
KEYWORD
nonn
AUTHOR
Dimitris Valianatos, Jan 12 2017
STATUS
approved