cp's OEIS Frontend

A336986 Numbers that are not Colombian and not Bogotá.

%I A336986 #18 Aug 25 2020 06:37:33
%S A336986 2,6,8,10,12,13,14,15,17,18,19,21,22,23,26,27,28,29,30,32,33,34,35,37,
%T A336986 38,40,41,43,44,45,46,47,48,50,51,52,54,55,57,58,59,60,61,62,63,65,66,
%U A336986 67,68,69,70,71,72,73,74,76,77,78,79,80,82,83,84,85,87,89,90,91
%N A336986 Numbers that are not Colombian and not Bogotá.
%C A336986 Equivalently, numbers m that are of the form k + sum of digits of k for some k (A176995), but are not of the form q * product of digits of q for any q.
%C A336986 As repunits are trivially Bogotá numbers, there are not repunits in the data.
%C A336986 A336983, A336984, A336985 and this sequence form a partition of the set of positive integers N*.
%H A336986 Giovanni Resta, <a href="http://www.numbersaplenty.com/set/self_number/">Self or Colombian number</a>, Numbers Aplenty.
%H A336986 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Coi#Colombian">Index to sequences related to Colombian numbers</a>.
%e A336986 13 = 11 + (1+1) is not Colombian and 13 is not of the form q * product of digits of q for any q <= 13, so 13 is not a Bogotá number, hence 13 is a term.
%e A336986 39 = 33 + (3+3) is not Colombian but 39 = 13 * (1*3) is a Bogotá number, hence 39 is not a term.
%e A336986 42 = 21 * (2*1) is a Bogotá number but there does not exist k < 42 such that 42 = k + sum of digits of k, hence 42 is a Colombian number and 42 is not a term.
%t A336986 m = 100; Intersection[Select[Union[Table[n + Plus @@ IntegerDigits[n], {n, 1, m}]], # <= m &], Complement[Range[m], Select[Union[Table[n * Times @@ IntegerDigits[n], {n, 1, m}]], # <= m &]]] (* _Amiram Eldar_, Aug 22 2020 *)
%o A336986 (PARI) lista(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), setminus([1..nn], Set(vector(nn, k, k*vecprod(digits(k))))))); \\ _Michel Marcus_, Aug 23 2020
%Y A336986 Cf. A003052 (Colombian), A176995 (not Colombian), A336826 (Bogotá), A336983 (Bogotá and not Colombian), A336984 (Bogotá and Colombian), A336985 (Colombian not Bogotá), this sequence (not Colombian and not Bogotá).
%K A336986 nonn,base
%O A336986 1,1
%A A336986 _Bernard Schott_, Aug 22 2020