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

Author

Sergio Pimentel, Sep 16 2008

Keywords

• base
• nonn

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

Examples

			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).
		

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

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).

Programs

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 *)

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

Extensions

Edited and extended by Klaus Brockhaus, Sep 19 2008