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A337731 a(n) is the smallest k >= 1 such that k*n is a Moran number.

%I A337731 #20 Sep 08 2022 08:46:25
%S A337731 18,9,6,21,9,3,3,19,2,19,18,7,9,3,3,37,9,1,6,199,1,9,9,37,199,6,1,3,9,
%T A337731 1663,12,937,6,1117,1657,1361,3,3,3,17497,18,1,12,10909,1,14563,9,
%U A337731 18541,17551,199999,3,3,18,87037,1108909,157141,2,154981,9,1483333
%N A337731 a(n) is the smallest k >= 1 such that k*n is a Moran number.
%C A337731 m is a Moran number if m /digsum(m) is a prime number (A001101).
%C A337731 a(n) = 1 if and only if n is a Moran number.
%e A337731 For n = 6, (1*6) / digsum(1*6) = 1, (2*6) / digsum(2*6) = 12 / 3 = 4, (3*6) / digsum(3*6) = 18 / 9 = 2 = prime(1), so a(6) = 3.
%e A337731 For n = 7, (1*7) / digsum(1*7) = 1, (2*7) / digsum(2*7) = 14 / 5, (3*7) / digsum(3*7) = 21 / 3 = 7 = prime(4), so a(7) = 3.
%t A337731 moranQ[n_] := PrimeQ[n / Plus @@ IntegerDigits[n]]; a[n_] := Module[{k = 1}, While[!moranQ[k*n], k++]; k]; Array[a, 60] (* _Amiram Eldar_, Sep 19 2020 *)
%o A337731 (Magma) moran:=func<n|n mod &+Intseq(n) eq 0 and IsPrime(n div &+Intseq(n))>;
%o A337731 a:=[]; for n in [1..60] do k:=1; while not moran(k*n) do k:=k+1; end while; Append(~a,k); end for; a;
%Y A337731 Cf. A001101, A007953, A144261.
%K A337731 nonn,base
%O A337731 1,1
%A A337731 _Marius A. Burtea_, Sep 18 2020