A336986 Numbers that are not Colombian and not Bogotá.

2, 6, 8, 10, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 87, 89, 90, 91

Offset

1,1

Comments

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.

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

A336983, A336984, A336985 and this sequence form a partition of the set of positive integers N*.

Links

Table of n, a(n) for n=1..68.

Giovanni Resta, Self or Colombian number, Numbers Aplenty.

Index to sequences related to Colombian numbers.

Example

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.
39 = 33 + (3+3) is not Colombian but 39 = 13 * (1*3) is a Bogotá number, hence 39 is not a term.
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.

Mathematica

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 *)

Prog

(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

Crossrefs

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).

Sequence in context: A028772 A325463 A121744 * A198832 A173634 A005795

Adjacent sequences: A336983 A336984 A336985 * A336987 A336988 A336989

Keyword

nonn,base

Author

Bernard Schott, Aug 22 2020

Status

approved