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A058901 Inconsummate numbers in base 5: no number is this multiple of the sum of its digits (in base 5).

%I A058901 #23 May 10 2023 10:44:29
%S A058901 16,22,28,46,56,58,68,74,76,80,106,108,110,118,128,136,138,140,146,
%T A058901 152,168,198,202,206,208,230,249,256,258,262,263,268,274,276,278,280,
%U A058901 284,286,288,290,292,294,296,298,302,318,323,324,326,336,338
%N A058901 Inconsummate numbers in base 5: no number is this multiple of the sum of its digits (in base 5).
%H A058901 Daniel Mondot, <a href="/A058901/b058901.txt">Table of n, a(n) for n = 1..33069</a>
%p A058901 For Maple code see A058906.
%t A058901 base=5; Do[k=n; While[Apply[Plus, IntegerDigits[k, base]] n!=k&&k<250n, k+=n]; If[k==250 n, Print[n]], {n, 1, 10^4}] (* _Vincenzo Librandi_, Nov 03 2016 *)
%o A058901 (Python)
%o A058901 from itertools import count, islice, combinations_with_replacement
%o A058901 from sympy.ntheory import digits
%o A058901 def A058901_gen(startvalue=1): # generator of terms >= startvalue
%o A058901     for n in count(max(startvalue,1)):
%o A058901         for l in count(1):
%o A058901             if 4*l*n < 5**(l-1):
%o A058901                 yield n
%o A058901                 break
%o A058901             for d in combinations_with_replacement(range(5),l):
%o A058901                 if (s:=sum(d)) > 0 and sorted(digits(s*n,5)[1:]) == list(d):
%o A058901                     break
%o A058901             else:
%o A058901                 continue
%o A058901             break
%o A058901 A058901_list = list(islice(A058901_gen(),20)) # _Chai Wah Wu_, May 10 2023
%Y A058901 Cf. A003635, A052491, A058898-A058907.
%K A058901 nonn,base
%O A058901 1,1
%A A058901 _N. J. A. Sloane_, Jan 09 2001