A144261 a(n) = smallest k such that k*n is a Niven (or Harshad) number.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 9, 3, 2, 3, 6, 1, 6, 1, 1, 5, 9, 1, 2, 6, 1, 3, 9, 1, 12, 6, 4, 3, 2, 1, 3, 3, 3, 1, 10, 1, 12, 3, 1, 5, 9, 1, 8, 1, 2, 3, 18, 1, 2, 2, 2, 9, 9, 1, 12, 6, 1, 3, 3, 2, 3, 3, 3, 1, 18, 1, 7, 3, 2, 2, 4, 2, 9, 1, 1, 5, 18, 1, 6, 6, 3, 3, 9, 1, 4, 5, 4, 9, 2, 2, 12, 4, 2, 1

Offset

1,11

Comments

Niven (or Harshad) numbers are numbers that are divisible by the sum of their digits.

Does a(n) exist for all n? - Klaus Brockhaus, Sep 19 2008

Links

David Radcliffe, Table of n, a(n) for n = 1..10000

David Radcliffe, Every positive integer divides a Harshad number

Eric Weisstein's World of Mathematics, Harshad Number

Example

a(14) = 3 since neither 1*14 or 2*14 are Niven numbers, but 3*14 = 42 is a Niven number: 42 = 7*(4+2).

Mathematica

niv[n_]:=Module[{k=1}, While[!Divisible[k*n, Total[IntegerDigits[ k*n]]], k++]; k]; Array[niv, 100] (* Harvey P. Dale, Jul 23 2016 *)

Prog

(PARI) digitsum(n) = {local(s=0); while(n, s+=n%10; n\=10); s}
{for(n=1, 100, k=1; while((p=k*n)%digitsum(p)>0, k++); print1(k, ", "))} /* Klaus Brockhaus, Sep 19 2008 */
(Python)
from itertools import count
def A144261(n): return next(filter(lambda k:not (m:=k*n) % sum(int(d) for d in str(m)), count(1))) # Chai Wah Wu, Nov 04 2022

Crossrefs

Cf. A005349 (Niven numbers), A144262 (smallest k such that k*n is not a Niven number), A144363 (records in A144261), A144364 (where records occur in A144261).

Sequence in context: A105162 A010184 A107830 * A337819 A046148 A231933

Adjacent sequences: A144258 A144259 A144260 * A144262 A144263 A144264

Keyword

base,nonn

Author

Sergio Pimentel, Sep 16 2008

Extensions

Edited and extended by Klaus Brockhaus, Sep 19 2008

Status

approved