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

1,1

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.

Links

Table of n, a(n) for n=1..60.

Example

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.

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 *)

Prog

(Magma) moran:=func<n|n mod &+Intseq(n) eq 0 and IsPrime(n div &+Intseq(n))>;
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;

Crossrefs

Cf. A001101, A007953, A144261.

Sequence in context: A264389 A104218 A033338 * A169736 A112876 A070703

Adjacent sequences: A337728 A337729 A337730 * A337732 A337733 A337734

Keyword

nonn,base

Author

Marius A. Burtea, Sep 18 2020

Status

approved