A248499 - OEIS

A248499

Numbers m that are coprime to A059995(m): floor(m/10).

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 31, 32, 34, 35, 37, 38, 41, 43, 45, 47, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 65, 67, 71, 72, 73, 74, 75, 76, 78, 79, 81, 83, 85, 87, 89, 91, 92, 94, 95, 97, 98, 101, 103, 107, 109, 111, 112

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Definition of "being coprime" and special-case conventions are as in Wikipedia. In particular, when m < 10 then floor(m/10) = 0, and zero is coprime only to 1. The complementary sequence is A248500. Note: The first 57 terms a(n) coincide with A069715, but the two sequences are different.

The limit mean density of these numbers exists and equals 1223/2100 = A250031(10)/A250033(10). - Stanislav Sykora, Dec 08 2014

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..20000

Stanislav Sykora, On some number densities related to coprimes, Stan's Library, Vol. V, Nov 2014, DOI: 10.3247/SL5Math14.005.

Wikipedia, Coprime integers.

FORMULA

{ m : gcd(m, floor(m/10)) = 1 }.

EXAMPLE

1 is a term because gcd(1,0) = 1.

123 is not a term because gcd(123,12) = 3.

165 is a term because 165 and 16 are coprime.

MATHEMATICA