A069715 -id:A069715 - cp's OEIS frontend

A052423 Highest common factor of nonzero digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 1

Offset: 1

Henry Bottomley, Mar 17 2000

			a(46) = 2 because the highest common factor of 4 and 6 is 2.
a(47) = 1 because the highest common factor of 4 and 7 is 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007954.

a052423 n = f n n where
   f x 1 = 1
   f x y | x < 10    = gcd x y
         | otherwise = if d == 1 then 1 else f x' (gcd d y)
         where (x', d) = divMod x 10
-- Reinhard Zumkeller, Apr 14 2014

a:= n-> igcd(subs(0=[][], convert(n, base, 10))[]):
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 04 2020

Table[Apply[GCD, IntegerDigits[n]], {n, 100}] (* Alonso del Arte, Apr 02 2020 *)

a(n) = my(d=digits(n)); gcd(select(x->(x!=0), d)); \\ Michel Marcus, Apr 04 2020

def euclGCD(a: Int, b: Int): Int = b match { case 0 => a; case n => Math.abs(euclGCD(b, a % b)) }
def digitGCD(n: Int) = n.toString.toCharArray.map( - 48).scanLeft(0)(euclGCD(, _)).last
(1 to 100).map(digitGCD()) // _Alonso del Arte, Apr 02 2020

a(A069715(n)) = 1. - Reinhard Zumkeller, Apr 14 2014

A248499 Numbers m that are coprime to A059995(m): floor(m/10).

Original entry on oeis.org

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

Offset: 1

Stanislav Sykora, Oct 07 2014

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

			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.

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.

Cf. A059995, A248500, A248501, A248502, A250031, A250033.

Select[ Range@ 120, GCD[#, Floor[#/10]] == 1 &] (* Robert G. Wilson v, Oct 22 2014 *)

a=vector(20000);
i=n=0;while(i++,if(gcd(i,i\10)==1,a[n++]=i;if(n==#a,break)));a

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

A240913 Numbers m such that GCD of digits of m is 1 and no digit of m is 1.

Original entry on oeis.org

23, 25, 27, 29, 32, 34, 35, 37, 38, 43, 45, 47, 49, 52, 53, 54, 56, 57, 58, 59, 65, 67, 72, 73, 74, 75, 76, 78, 79, 83, 85, 87, 89, 92, 94, 95, 97, 98, 203, 205, 207, 209, 223, 225, 227, 229, 230, 232, 233, 234, 235, 236, 237, 238, 239, 243, 245, 247, 249

Offset: 1

Reinhard Zumkeller, Apr 14 2014

A052423(a(n)) = 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Subsequence of A069715.

a240913 n = a240913_list !! (n-1)
a240913_list = filter (not . elem '1' . show) a069715_list

gcdQ[n_]:=Module[{idn=IntegerDigits[n]},!MemberQ[idn,1]&&GCD@@idn==1]; Select[ Range[300],gcdQ] (* Harvey P. Dale, Dec 17 2014 *)

is(n)=my(d=Set(digits(n))); setsearch(d,1)==0 && gcd(d)==1 \\ Charles R Greathouse IV, Nov 01 2014

A350494 Divide n by the greatest common divisor of the nonzero digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 10, 31, 32, 11, 34, 35, 12, 37, 38, 13, 10, 41, 21, 43, 11, 45, 23, 47, 12, 49, 10, 51, 52, 53, 54, 11, 56, 57, 58, 59, 10, 61, 31, 21, 32, 65, 11, 67

Offset: 1

Rémy Sigrist, Jan 01 2022

			a(42) = 42 / gcd(4, 2) = 42 / 2 = 21.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A052423, A069715.

PARI
```
a(n) = n / gcd(digits(n))
```

from math import gcd
def a(n): return n//gcd(*[int(d) for d in str(n)])
print([a(n) for n in range(1, 68)]) # Michael S. Branicky, Jan 01 2022

a(n) = n / A052423(n).
a(n) = n iff n belongs to A069715.
a(a(n)) = a(n).

A078453 Numbers in which all the digits are coprime to each other.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 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

Offset: 1

Amarnath Murthy, Nov 28 2002

Cf. A069715.

Join[Range[0,9],Select[Range[10,98],GCD@@IntegerDigits[#]==1 &]] (* Stefano Spezia, Dec 23 2022 *)

from math import gcd
from functools import reduce
def ok(n):
    d = list(map(int, str(n)))
    return len(d) == 1 or reduce(gcd, d) == 1
print([k for k in range(100) if ok(k)]) # Michael S. Branicky, Dec 23 2022

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A052423 Highest common factor of nonzero digits of n.

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A248499 Numbers m that are coprime to A059995(m): floor(m/10).

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A240913 Numbers m such that GCD of digits of m is 1 and no digit of m is 1.

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A350494 Divide n by the greatest common divisor of the nonzero digits of n.

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PARI

Python

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A078453 Numbers in which all the digits are coprime to each other.

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Author

Keywords

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Programs

Mathematica

Python