A342810 Numbers k that divide the smallest number whose sum of digits is k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 27, 81, 191, 243, 729, 999, 2187, 2997, 6561, 8991, 19683, 26973, 33321, 36963, 39049, 59049, 80919, 100389, 110889, 118827, 177147, 177897, 183951, 242757, 332667, 356481, 531441, 551853, 728271, 998001, 1069443, 1367631, 1594323, 1655559, 2184813

Offset: 1

Author

Ruediger Jehn, Mar 22 2021

Keywords

• nonn
• base

Comments

By definition, if k divides A051885(k), then k is a term of this sequence.

From Ruediger Jehn, Jun 17 2021: (Start)

None of the terms is divisible by 2*5*11*13.

If a term x has the form 3^m * y where m > 1 (which is the case for the overwhelming number of terms of this sequence), then all prime factors of y are terms of A066364.

If a term x has the form 3^m * p * q where m > 1, where p is a term of A066364 and where q is the product of all other factors of the prime factorization of x, then all numbers 3^m * p^i * q are also terms for any integer i. (End)

Examples

			21 is a term because the smallest number with a digital sum of 21 is 399 (A051885(21) = 399) which is divisible by 21.
		

Links

• Kester Habermann, Table of n, a(n) for n = 1..792 (first 200 terms from Chai Wah Wu)
• Rüdiger Jehn and Kester Habermann, Properties of terms of OEIS A342810, arXiv:2106.05866 [math.GM], 2021.

Crossrefs

Cf. A007953, A051885, A066364.

Programs

PARI

MAX=10000; for (e = 0, MAX, for (d = 1, 9, k =(d+1)*10^e - 1; x = d+9*e; if (k%x==0, print1(x, ", ");)))

Python

A342810_list = [n for n in range(1,10**6) if n==1 or ((n % 9)+1)*pow(10,n//9,n) % n == 1] # Chai Wah Wu, Apr 04 2021

Extensions

Name clarified by Jon E. Schoenfield, Apr 27 2021