%I #15 Jun 24 2013 17:00:38

%S 2,21,14,15,21,35,33,39,65,51,57,95,69,115,86,87,93,155,217,111,122,

%T 123,129,215,141,235,158,159,265,371,177,183,194,427,201,335,213,219,

%U 365,511,237,395,249,415,446,267,278,623,1246,291,302,303,309,515,321

%N Smallest number k such that the sum of the distinct prime divisors of k equals n times a prime.

%C Smallest k such that sopf(k) = n*p, p prime.

%H Alois P. Heinz, <a href="/A212483/b212483.txt">Table of n, a(n) for n = 1..5000</a>

%e a(5) = 21 because 21 = 3*7 and 3 + 7 = 10 = 5*2 where 2 is prime.

%p with (numtheory):

%p sopf:= proc(n) option remember;

%p add(i, i=factorset(n))

%p end:

%p a:= proc(n) local k, p;

%p for k from 2 while irem(sopf(k), n, 'p')>0 or

%p not isprime(p) do od; k

%p end:

%p seq (a(n), n=1..100); # _Alois P. Heinz_, Jun 03 2012

%t snk[n_]:=Module[{k=1},While[!PrimeQ[(Total[Transpose[ FactorInteger[k]] [[1]]])/n],k++];k]; Array[snk,60] (* _Harvey P. Dale_, Jun 24 2013 *)

%Y Cf. A008472, A213020.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jun 02 2012