# [seqfan] Need help with Colombian numbers etc.

Neil Sloane njasloane at gmail.com
Sat Oct 12 18:37:33 CEST 2013

```Consider the map f(n) = n + (sum of digits of n) (see A062028, A007953).
Let g(m) = number of n such that f(n) = m (i.e. the number of inverses of
m), A230093.
Numbers m with g(m) = 0 are called the Self or Colombian numbers, A003052.
Numbers m with g(m) = 1 give A225793.
Numbers m with g(m) = 2 give A230094.
The following paper:
Narasinga Rao, A. On a technique for obtaining numbers with a multiplicity
of generators. Math. Student 34 1966 79--84 (1967). MR0229573 (37 #5147)
seems to say that the sequence
Numbers m with g(m) = 3
begins with 10^13 + 1, but I may have misread it.
Certainly 9999999999892, 9999999999901 and 10000000000000 all have f(n) =
10000000000001, so that number has at least 3 inverses.
In any case Narasinga Rao's assertion should be checked.
Could someone compute the first few terms of "Numbers m with g(m) = 3"?

In base two the analogs of these sequences are respectively
A092391, A000120, A228085, A010061, A222088, A230091, A230092.

Neil

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.