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A105212 a(1) = 668; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).

%I A105212 #16 Aug 18 2017 03:17:24
%S A105212 668,838,1260,1278,1355,1632,1655,1992,2081,2082,2435,2928,2995,3600,
%T A105212 3611,3792,3877,3878,4165,4195,5040,5058,5345,6420,6538,7015,7105,
%U A105212 7147,8176,8259,11016,11039,11149,11150,11381,12000,12011,12012,12049,12050
%N A105212 a(1) = 668; for n > 1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
%C A105212 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 A105212 T. D. Noe, <a href="/A105212/b105212.txt">Table of n, a(n) for n = 1..2000</a>
%H A105212 Doug Engel, <a href="http://www.jstor.org/stable/2689298">Problem 886</a>, Math. Mag., 48 (1975), 57-58.
%e A105212 a(2)=838 because a(1)=668, the distinct prime factors of a(1) are 2 and 167; finally, 1 + 668 + 2 + 167 = 838.
%p A105212 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]:=668: 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
%o A105212 (Haskell)
%o A105212 a105212 n = a105212_list !! (n-1)
%o A105212 a105212_list = 668 : map
%o A105212       (\x -> x + 1 + sum (takeWhile (< x) $ a027748_row x)) a105212_list
%o A105212 -- _Reinhard Zumkeller_, Jan 15 2015
%Y A105212 Cf. A003508, A027748, A105210, A105211, A105213.
%K A105212 nonn,easy
%O A105212 1,1
%A A105212 _R. K. Guy_, Apr 14 2005
%E A105212 More terms from _Robert G. Wilson v_ and _Emeric Deutsch_, Apr 14 2005