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a(1) = 2. a(n) is the smallest number in A349484, which is not an earlier term and for which a(n-1) + a(n) is in A349484.
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%I #10 Sep 08 2022 08:46:26

%S 2,3,4,5,225,18,9,27,21,6,48,108,72,36,156,54,81,111,400,7,20,210,306,

%T 135,153,288,112,224,100,8,10,902,1168,192,324,180,50,230,900,201,280,

%U 420,209,511,407,481,702,216,405,243,378,486,432,480,621,351,513,648

%N a(1) = 2. a(n) is the smallest number in A349484, which is not an earlier term and for which a(n-1) + a(n) is in A349484.

%e a(1) = 2 and a(2) = 3 are Niven numbers with derivatives 2' = 1 and 3' = 1 which are Niven numbers, and a(1) + a(2) = 2 + 3 = 5 which is Niven number and 5' = 1 is also a Niven number.

%o (Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; a:=[]; niven:=func<n|n mod &+Intseq(n) eq 0 >; ff:=func<n|niven(n) and niven(Floor(f(n)))>; a:=[2]; for n in [2..58] do k:=3; while k in a or not(ff(k) and ff(k+a[n-1])) do k:=k+1; end while; Append(~a,k); end for; a;

%Y Cf. A003415 (arithmetic derivative), A005349 (Niven numbers), A349484.

%K nonn,base

%O 1,1

%A _Marius A. Burtea_, Nov 20 2021