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A058906 Inconsummate numbers in base 11: no number is this multiple of the sum of its digits (in base 11).

%I A058906 #17 May 09 2023 19:05:59
%S A058906 68,70,79,80,82,92,104,200,202,212,214,224,225,248,260,314,320,332,
%T A058906 380,392,452,458,464,490,502,508,512,513,514,518,520,524,530,562,568,
%U A058906 574,578,579,580,584,585,590,592,595,598,599,622,628,634,635
%N A058906 Inconsummate numbers in base 11: no number is this multiple of the sum of its digits (in base 11).
%p A058906 digitsum := proc (n,b) local i; add(i,i=convert(n,base,b)) end; b := 11:N := 43922; L := []: for n from 1 to N do k := digitsum(n,b): if (n mod k)=0 then L := [op(L), n/k] fi: od: M := []: for i from 1 to 1000 do if not(member(i,L)) then M := [op(M),i] fi od: lprint(M);
%t A058906 base = 11; Do[k = n; While[ Apply[ Plus, IntegerDigits[k, base] ]*n != k && k < 250n, k += n]; If[k == 250n, Print[n] ], {n, 1, 10^3} ]
%o A058906 (Python)
%o A058906 from itertools import count, islice, combinations_with_replacement
%o A058906 from sympy.ntheory import digits
%o A058906 def A058906_gen(startvalue=1): # generator of terms >= startvalue
%o A058906     for n in count(max(startvalue,1)):
%o A058906         for l in count(1):
%o A058906             if 10*l*n < 11**(l-1):
%o A058906                 yield n
%o A058906                 break
%o A058906             for d in combinations_with_replacement(range(11),l):
%o A058906                 if (s:=sum(d)) > 0 and sorted(digits(s*n,11)[1:]) == list(d):
%o A058906                     break
%o A058906             else:
%o A058906                 continue
%o A058906             break
%o A058906 A058906_list = list(islice(A058906_gen(),20)) # _Chai Wah Wu_, May 09 2023
%Y A058906 Cf. A003635, A052491, A058898-A058907.
%K A058906 nonn,base
%O A058906 1,1
%A A058906 _N. J. A. Sloane_, Jan 09 2001