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

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, 1663, 12, 937, 6, 1117, 1657, 1361, 3, 3, 3, 17497, 18, 1, 12, 10909, 1, 14563, 9, 18541, 17551, 199999, 3, 3, 18, 87037, 1108909, 157141, 2, 154981, 9, 1483333

Offset: 1

Author

Marius A. Burtea, Sep 18 2020

Keywords

• nonn
• base

Comments

m is a Moran number if m /digsum(m) is a prime number (A001101).

a(n) = 1 if and only if n is a Moran number.

Examples

			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.
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.
		

Crossrefs

Cf. A001101, A007953, A144261.

Programs

Magma

moran:=func;
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;

Mathematica

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 *)