A213015 - OEIS

%I #6 Jun 04 2012 21:33:17

%S 4,8,9,21,25,30,32,33,36,49,57,69,70,84,85,93,100,102,120,121,128,129,

%T 133,135,144,145,162,169,174,177,182,190,205,213,217,228,237,238,246,

%U 249,253,260,265,286,289,308,309,310,312,318,340,351,361,372,393,406

%N Numbers n such that the sum of prime factors of n (counted with multiplicity) is 2 times a prime.

%C The numbers A100118(n)^2 are in the sequence.

%F sopfr(n) = 2*p, p prime.

%e 36 is in the sequence because 36 = 2^2 * 3^2 => sum of prime factors = 2*2+3*2 = 10 = 2*5 where 5 is prime.

%p with(numtheory):A:= proc(n) local e, j; e := ifactors(n)[2]: add (e[j][1]*e[j][2], j=1..nops(e)) end: for m from 1 to 3000 do: if type(A(m)/2,prime)= true then printf(`%d, `,m):else fi:od:

%t L = {}; Do[ww = Transpose[FactorInteger[k]]; w = ww[[1]].ww[[2]]; If[PrimeQ[w/2], AppendTo[L, k]], {k, 2, 500}]; L

%Y Cf. A001414, A100118.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jun 02 2012