A058905 Inconsummate numbers in base 9: no number is this multiple of the sum of its digits (in base 9).

46, 47, 48, 56, 58, 66, 76, 86, 136, 138, 167, 176, 222, 227, 228, 248, 258, 298, 302, 308, 312, 316, 318, 338, 343, 344, 347, 348, 352, 354, 356, 358, 362, 374, 383, 384, 392, 398, 402, 403, 404, 406, 407, 408, 411, 412, 414, 416, 422, 423

Offset: 1

Author

N. J. A. Sloane, Jan 09 2001

Keywords

• nonn
• base

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

Maple

For Maple code see A058906.

Python

from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058905_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if l*n<<3 < 9**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(9),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,9)[1:]) == list(d):
                    break
            else:
                continue
            break
A058905_list = list(islice(A058905_gen(),20)) # Chai Wah Wu, May 10 2023