A349485 - OEIS

%I #14 Sep 08 2022 08:46:26

%S 18,27,153,803,1101,1503,1926,3070,3077,3546,4577,6246,6315,8717,

%T 10566,11646,14093,15310,15426,18456,24936,30617,33576,34326,43079,

%U 50418,59026,62004,69781,71009,71802,72587,74616,77593,80118,94056,110138,111546,112626,113166

%N Moran numbers whose arithmetic derivative is also a Moran number (A001101).

%C Conjecture: The sequence is infinite.

%e 18 = A001101(1) and 18' = 21 = A001101(2), so 18 is a term.

%e 153 = A001101(13) and 153' = 111 = A001101(8), so 153 is a term.

%t moranQ[n_] := PrimeQ[n / Plus @@ IntegerDigits[n]]; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[120000], And @@ moranQ /@ {#, d[#]} &] (* _Amiram Eldar_, Nov 20 2021 *)

%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)]]) >; moran:=func<n|n mod &+Intseq(n) eq 0 and IsPrime(n div &+Intseq(n))>; [n:n in [2..114000]| moran(n) and moran(Floor(f(n)))];

%Y Cf. A001101 (Moran number), A003415 (arithmetic derivative).

%K nonn,base

%O 1,1

%A _Marius A. Burtea_, Nov 20 2021