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A335859 Terms of A334245 in increasing order and without repetition.

%I A335859 #46 May 08 2021 08:30:09
%S A335859 12,15,21,30,35,57,60,65,70,77,91,105,111,114,119,126,133,143,147,150,
%T A335859 155,165,168,180,185,190,198,209,217,220,231,234,255,260,264,294,301,
%U A335859 310,312,319,323,330,341,360,427,432,437,455,456,462,473,497,504,510,511,546,559,588
%N A335859 Terms of A334245 in increasing order and without repetition.
%C A335859 See the network with the 50 smallest merging points of A334245 in link.
%H A335859 Robert Israel, <a href="/A335859/b335859.txt">Table of n, a(n) for n = 1..5939</a>
%H A335859 Bernard Schott and Blandine Schott, <a href="/A335859/a335859_3.pdf">Network of merging points</a>.
%e A335859 l means: add least prime factor, and,
%e A335859 L means: add largest prime factor.
%e A335859 For 3:
%e A335859    L:  3 + 3 = 6            l: 3 + 3 = 6
%e A335859    l:  6 + 2 = 8            L: 6 + 3 = 9
%e A335859    L:  8 + 2 = 10           l: 9 + 3 = 12
%e A335859    l: 10 + 2 = 12
%e A335859 So A334245(3) = 12 and 12 is a merging point with a(1) = 12.
%e A335859 Now, for 12:
%e A335859    L: 12 + 3 = 15           l: 12 + 2 = 14
%e A335859    l: 15 + 3 = 18           L: 14 + 7 = 21
%e A335859    L: 18 + 3 = 21
%e A335859 So A334245(12) = 21 and 21 is the merging point corresponding to 12 with a(3) = 21.
%p A335859 N:= 1000: # to get all values <= N
%p A335859 S:= x -> x + min(numtheory:-factorset(x)):
%p A335859 T:= x -> x + max(numtheory:-factorset(x)):
%p A335859 f:= proc(n) g(S(n),T(n),0,1) end proc:
%p A335859 g:= proc(s,t,i,j) option remember;
%p A335859       if max(s,t) > N then return 0 fi;
%p A335859       if s = t and i=j then return s fi;
%p A335859       if s <= t then
%p A335859         if i = 0 then procname(T(s),t,1,j)
%p A335859         else procname(S(s),t,0,j)
%p A335859         fi
%p A335859       elif j=0 then procname(s,T(t),i,1)
%p A335859       else procname(s,S(t),i,0)
%p A335859       fi
%p A335859 end proc:
%p A335859 sort(convert(map(f, {$2..N}) minus {0},list)); # _Robert Israel_, Jul 09 2020
%Y A335859 Cf. A334245.
%K A335859 nonn
%O A335859 1,1
%A A335859 _Bernard Schott_, Jun 27 2020