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%I #7 Sep 08 2022 08:46:08
%S 54023,54203,500407,23456789,23458679,23459687,23465789,23465987,
%T 23469587,23475869,23478569,23489657,23495867,23496587,23498567,
%U 23546879,23546987,23548697,23564897,23564987,23567849,23569487,23576489,23584679,23587649,23589647,23594687
%N Numbers n such that A243361(n) = 123456789.
%C Supersequence of A243363, A243364 and A160402.
%C Conjecture 1: sequence is infinite.
%C Conjecture 2: a(1), a(2) and a(3) are composites; there are no other numbers n > 3 such that a(n) = composite number.
%F a(1) = 54023; a(2) = 54203; a(3) = 500407; a(4) … a(3101) = A160402; a(3102) ... a(22659) = A243363; ....
%e Sets of divisors of a(n): (1, 89, 607, 54023); (1, 67, 809, 54203); (1, 83, 6029, 500407); (1, 23456789); …
%o (Magma) [n: n in [1..1000000] | Seqint(Reverse(Sort(&cat[(Intseq(k)): k in Divisors(n)]))) eq 123456789]
%Y Cf. A160402, A243360, A243361, A243363, A243364.
%K nonn,base
%O 1,1
%A _Jaroslav Krizek_, Jun 04 2014