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A003635 Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10).

%I A003635 M5325 #34 Nov 30 2024 19:23:29
%S A003635 62,63,65,75,84,95,161,173,195,216,261,266,272,276,326,371,372,377,
%T A003635 381,383,386,387,395,411,416,422,426,431,432,438,441,443,461,466,471,
%U A003635 476,482,483,486,488,491,492,493,494,497,498,516,521,522,527,531,533,536
%N A003635 Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10).
%D A003635 J. H. Conway, personal communication.
%D A003635 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003635 Daniel Mondot, <a href="/A003635/b003635.txt">Table of n, a(n) for n = 1..10867</a>
%H A003635 Giovanni Resta, <a href="http://www.numbersaplenty.com/set/inconsummate_number/">Numbers Aplenty: Inconsummate numbers</a>
%p A003635 For Maple code see A058906.
%t A003635 nmax = 1000; Reap[ Do[k = n; kmax = 100*n; While[ Tr[ IntegerDigits[k]]*n != k && k < kmax, k = k + n]; If[k == kmax, Sow[n]], {n, 1, nmax}]][[2, 1]] (* _Jean-François Alcover_, Jul 12 2012 *)
%o A003635 (Python)
%o A003635 from itertools import count, islice, combinations_with_replacement
%o A003635 def A003635_gen(startvalue=1): # generator of terms >= startvalue
%o A003635     for n in count(max(startvalue,1)):
%o A003635         for l in count(1):
%o A003635             if 9*l*n < 10**(l-1):
%o A003635                 yield n
%o A003635                 break
%o A003635             for d in combinations_with_replacement(range(10),l):
%o A003635                 if (s:=sum(d))>0 and sorted(str(s*n)) == [str(e) for e in d]:
%o A003635                     break
%o A003635             else:
%o A003635                 continue
%o A003635             break
%o A003635 A003635_list = list(islice(A003635_gen(),20)) # _Chai Wah Wu_, May 09 2023
%Y A003635 Cf. A003634, A052489, A052490, A052491, A058898-A058917.
%K A003635 nonn,easy,nice,base
%O A003635 1,1
%A A003635 _N. J. A. Sloane_ and _Mira Bernstein_