This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A213015 #6 Jun 04 2012 21:33:17
%S A213015 4,8,9,21,25,30,32,33,36,49,57,69,70,84,85,93,100,102,120,121,128,129,
%T A213015 133,135,144,145,162,169,174,177,182,190,205,213,217,228,237,238,246,
%U A213015 249,253,260,265,286,289,308,309,310,312,318,340,351,361,372,393,406
%N A213015 Numbers n such that the sum of prime factors of n (counted with multiplicity) is 2 times a prime.
%C A213015 The numbers A100118(n)^2 are in the sequence.
%F A213015 sopfr(n) = 2*p, p prime.
%e A213015 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 A213015 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 A213015 L = {}; Do[ww = Transpose[FactorInteger[k]]; w = ww[[1]].ww[[2]]; If[PrimeQ[w/2], AppendTo[L, k]], {k, 2, 500}]; L
%Y A213015 Cf. A001414, A100118.
%K A213015 nonn
%O A213015 1,1
%A A213015 _Michel Lagneau_, Jun 02 2012