A336985 Colombian numbers that are not Bogotá numbers.

3, 5, 7, 20, 31, 53, 86, 97, 108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 211, 222, 233, 244, 266, 277, 288, 299, 310, 323, 334, 345, 356, 367, 389, 400, 411, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 514, 536, 547, 558, 569, 580, 591, 602, 613

Offset: 1

Author

Bernard Schott, Aug 26 2020

Keywords

• nonn
• base

Comments

Equivalently, numbers m that are not of the form k + sum of digits of k for any k (A003052), and that are not of the form q * product of digits of q for any q (complement of A336826).

As repunits are trivially Bogotá numbers, there are not repunits in the data.

A336983, A336984, A336986 and this sequence form a partition of the set of positive integers N*

Examples

			7 is a term because there are not k < 7  such that 7 = k + sum of digits of k, and that are not q such that 7 = q * product of digits of q.
13 is not of the form q * product of digits of q for any q <= 13, so 13 is not a Bogotá number, but 13 = 11 + (1+1) is not Colombian, hence 13 is not a term.
42 is Colombian because there does not exist m < 42 such that 42 = m + sum of digits of m, but as 42 = 21 * (2*1) is a Bogota number, 42 is not a term.
		

Links

• Giovanni Resta, Self or Colombian number, Numbers Aplenty.
• Index to sequences related to Colombian or self numbers.

Crossrefs

Cf. A003052 (Colombian), A176995 (not Colombian), A336826 (Bogotá numbers), A336983 (Bogotá not Colombian), A336984 (Bogotá and Colombian), this sequence (Colombian not Bogotá), A336986 (not Colombian and not Bogotá).

Programs

Mathematica

m = 600; Intersection[Complement[Range[m], 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 26 2020 *)

PARI

lista(nn) = Vec(setintersect(setminus([1..nn], Set(vector(nn, k, k+sumdigits(k)))), setminus([1..nn], Set(vector(nn, k, k*vecprod(digits(k))))))); \\ Michel Marcus, Aug 26 2020