%I A003508 M0580
%S A003508 1,2,3,4,7,8,11,12,18,24,30,41,42,55,72,78,97,98,108,114,139,140,155,
%T A003508 192,198,215,264,281,282,335,408,431,432,438,517,576,582,685,828,857,
%U A003508 858,888,931,958,1440,1451,1452,1469,1596,1628,1679,1776,1819,1944
%N A003508 a(1) = 1; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors 
               of a(n-1) that are < a(n-1).
%C A003508 R. K. Guy reports, Apr 14 2005: In Math. Mag. 48 (1975) 301 one finds 
               "C. W. Trigg, C. C. Oursler and R. Cormier & 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.
%C A003508 This suggests that there may be infinitely many different (non-merging) 
               sequences obtained by choosing different starting values.
%C A003508 All terms of these five sequences are distinct up to least 10^30. - T. 
               D. Noe, Oct 19 2007
%D A003508 Problem 886, Math. Mag., 48 (1975), 57-58.
%D A003508 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003508 T. D. Noe, <a href="b003508.txt">Table of n, a(n) for n=1..2000</a>
%e A003508 a(6)=8, so a(7) = 8 + 1 + 2 = 11.
%t A003508 a[1] = 1; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ 
               #[[1]], {1}] & /@ FactorInteger[ a[n - 1]]], # < a[n - 1] &]; Table[ 
               a[n], {n, 54}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 13 
               2005)
%Y A003508 Cf. A096460, A105221, A105233
%Y A003508 Sequence in context: A089190 A065294 A026808 this_sequence A078662 A050048 
               A122456
%Y A003508 Adjacent sequences: A003505 A003506 A003507 this_sequence A003509 A003510 
               A003511
%K A003508 nonn,nice,easy
%O A003508 1,2
%A A003508 N. J. A. Sloane (njas(AT)research.att.com).
%E A003508 More terms from Henry Bottomley (se16(AT)btinternet.com), May 09 2000