%I #48 Aug 22 2020 05:56:57
%S 4,11,16,24,25,36,39,49,56,81,88,93,96,111,119,138,144,164,171,192,
%T 224,242,250,297,336,339,366,393,408,422,448,456,488,497,516,520,522,
%U 564,575,696,704,744,755,777,792,795,819,848,884,900,912,933,944,966,992
%N Bogota numbers that are not Colombian numbers.
%C Equivalently, numbers m that are of the form k + sum of digits of k for some k (A176995), and also of the form q * product of digits of q for some q (A336826).
%C Repunits are trivially Bogota numbers but the indices m of the repunits R_m that are not Colombian numbers are in A337139; also, all known repunit primes are terms (A004023) [see examples for primes R_2, R_19 and R_23].
%C 35424 is the smallest term that belongs to both A230094 and A336944 (see last example).
%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/self_number/">Self or Colombian number</a>, Numbers Aplenty.
%H Puzzling Stackexchange, <a href="https://puzzling.stackexchange.com/questions/98998/pairs-of-bogot%c3%a1-numbers?noredirect=1#comment281441_98998">Pairs of Bogotá Numbers</a>.
%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Coi#Colombian">Index to sequences related to Colombian numbers</a>.
%e R_2 = 11 = 10 + (1+0) = 11 * (1*1) is a term;
%e 24 = 21 + (2+1) = 12 * (1*2) is a term;
%e 39 = 33 + (3+3) = 13 * (1*3) is a term;
%e R_19 = 1111111111111111079 + (16*1+7+9) = 1111111111111111111 * (1^19) hence R_19 is a term;
%e R_23 = 11111111111111111111077 + (20*1+7+7) = 11111111111111111111111 * (1^23) hence R_23 is a term;
%e 42 = 21 * (2*1) is a Bogota number but there does not exist m < 42 such that 42 = m + sum of digits of m, hence 42 that is also a Colombian number is not a term.
%e 35424 = 35406 + (3+5+4+0+6) = 35397 + (3+5+3+9+7) = 2214 * (2*2*1*4) = 492 * (4*9*2).
%t m = 1000; Intersection[Select[Union[Table[n + Plus @@ IntegerDigits[n], {n, 1, m}]], # <= m &], Select[Union[Table[n * Times @@ IntegerDigits[n], {n, 1, m}]], # <= m &]] (* _Amiram Eldar_, Aug 10 2020 *)
%o (PARI) lista(nn) = Vec(setintersect(Set(vector(nn, k, k+sumdigits(k))), Set(vector(nn, k, k*vecprod(digits(k)))))); \\ _Michel Marcus_, Aug 20 2020
%Y Intersection of A176995 and A336826.
%Y Cf. A003052 (Colombian), A336984 (Bogota and Colombian), A336985 (Colombian not Bogota), A336986 (not Colombian and not Bogota).
%Y Cf. A230093, A230094, A336944, A337139.
%K nonn,base
%O 1,1
%A _Bernard Schott_, Aug 10 2020