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A342810
Numbers k that divide the smallest number whose sum of digits is k.
2
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
1,2
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)
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.
EXAMPLE
21 is a term because the smallest number with a digital sum of 21 is 399 (A051885(21) = 399) which is divisible by 21.
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ruediger Jehn, Mar 22 2021
EXTENSIONS
Name clarified by Jon E. Schoenfield, Apr 27 2021
STATUS
approved