%I #55 Sep 09 2015 16:29:50
%S 2,3,7,43,13,53,5,6221671,38709183810571,25621,10300271,2731,
%T 1079927141307582051252331702244209088763871
%N a(1)=2; thereafter a(n) = mpf(1+Product_{k=1..n-1} a(k)), where mpf(n) = f-th prime factor with multiplicity of n, for f=ceiling(bigomega(n)/2).
%H Anders Hellström, <a href="/A261564/a261564_1.rb.txt">Ruby program</a>
%F a(1)=2; thereafter a(n) = A079879(1+Product_{k=1..n-1}a(k)).
%t f[n_] := Block[{p = Flatten[Table[#1, {#2}] & @@@ FactorInteger@ n], len}, len = Length@ p; Which[n == 1, 1, OddQ@len, p[[1 + Floor[len/2]]], True, p[[len/2]]]]; a = {2}; Do[AppendTo[a, f[1 + Product[a[[k]], {k, 1, n - 1}]]], {n, 2, 13}] ; a (* _Michael De Vlieger_, Aug 25 2015 *)
%o (PARI) factorsm(n)=my(v=factor(n), f=factor(n)[, 1]~, w=[]); for(i=1, #f, for(j=1, v[i, 2], w=concat(w, f[i]))); w;
%o mpf(n)=my(f=factorsm(n)); f[ceil(#f/2)]
%o first(m)=my(v=vector(m)); v[1]=2; for(i=2, m, v[i]=mpf(1+prod(j=1, i-1, v[j]))); v;
%Y Cf. A079879, A001222, A000945, A000946.
%K nonn,more
%O 1,1
%A _Anders Hellström_, Aug 24 2015
%E a(13) from _Michael De Vlieger_, Aug 25 2015