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%I #23 Apr 20 2016 10:41:02
%S 1,2,3,5,11,13,12,47,49,24,167,169,503,505,1511,1513,912,432,5879,
%T 5881,600,97,204,118,512,87,148,3886,23291,23293,71,896,11812,60,
%U 41359,2394,11508,5529,8977,200,152681,152683,604,16996,635,40,257,957,79594,517,10155
%N a(n) is the sum of the prime factors, with repetition, of the sum of all preceding terms, with initial terms a(1)=1 and a(2)=2.
%H Paolo P. Lava, <a href="/A269004/b269004.txt">Table of n, a(n) for n = 1..2000</a>
%t a = {1, 2}; Do[AppendTo[a, Total@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ Total@ a, {1}]], {n, 3, 60}]; a (* _Michael De Vlieger_, Feb 19 2016 *)
%o (PARI) lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); print1(va[2] = 2, ", "); sp = vecsum(va); for (k=3, nn, f = factor(sp); va[k] = sum(j=1, #f~, f[j, 1]*f[j, 2]); print1(va[k], ", "); sp += va[k]; ); } \\ _Michel Marcus_, Feb 19 2016
%Y Cf. A001414, A268868 (similar sequence with initial terms 1,1).
%K nonn
%O 1,2
%A _David James Sycamore_, Feb 17 2016
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