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A105213 a(1) = 932; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).

%I A105213 #21 Aug 18 2017 03:17:33
%S A105213 932,1168,1244,1558,1621,1622,2436,2478,2550,2578,3870,3924,4039,4624,
%T A105213 4644,4693,4726,4885,5868,6037,6038,9060,9222,9310,9344,9420,9588,
%U A105213 9658,10111,10112,10194,11899,12136,12217,12880,12918,15077,15078,15450
%N A105213 a(1) = 932; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
%C A105213 In Math. Mag. 48 (1975) 301 one finds "C. W. Trigg, C. C. Oursler and R. Cormier and J. L. Selfridge have sent calculations on Problem 886 [Nov 1973] for which we had received only partial results [Jan 1975]. Cormier and Selfridge sent the following results: There appear to be five sequences beginning with integers less than 1000 which do not merge. These sequences were carried out to 10^8 or more." The five sequences are A003508, A105210-A105213.
%H A105213 T. D. Noe, <a href="/A105213/b105213.txt">Table of n, a(n) for n = 1..2000</a>
%H A105213 Doug Engel, <a href="http://www.jstor.org/stable/2689298">Problem 886</a>, Math. Mag., 48 (1975), 57-58.
%e A105213 a(2)=1168 because a(1)=932, the distinct prime factors of a(1) are 2 and 233; finally, 1 + 932 + 2 + 233 = 1168.
%p A105213 with(numtheory): p:=proc(n) local nn,ct,s: if isprime(n)=true then s:=0 else nn:=convert(factorset(n),list): ct:=nops(nn): s:=sum(nn[j],j=1..ct):fi: end: a[1]:=932: for n from 2 to 46 do a[n]:=1+a[n-1]+p(a[n-1]) od:seq(a[n],n=1..46); # _Emeric Deutsch_, Apr 14 2005
%t A105213 nx[n_]:=n+1+Total[Select[Transpose[FactorInteger[n]][[1]],#<n&]]; NestList[nx,932,40] (* _Harvey P. Dale_, Jul 24 2011 *)
%o A105213 (Haskell)
%o A105213 a105213 n = a105213_list !! (n-1)
%o A105213 a105213_list = 932 : map
%o A105213       (\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a105213_list
%o A105213 -- _Reinhard Zumkeller_, Jan 15 2015
%Y A105213 Cf. A027748, A003508, A105210, A105211, A105212.
%K A105213 nonn,easy
%O A105213 1,1
%A A105213 _R. K. Guy_, Apr 14 2005
%E A105213 More terms from _Robert G. Wilson v_ and _Emeric Deutsch_, Apr 14 2005