Draw a phi triangle

Question

Clarification: Basically, you need to make this

Euler's totient function has the name phi.

Let's try to calculate phi(8)

First, list all numbers 8 and under backwards, not including 0 or under

8
7
6
5
4
3
2
1

Now find which numbers don't share a factor with 8 (1 doesn't count), and place a # in their place.

8
#
6
#
4
#
2
#

Remove the numbers.

#

#

#

#
                                                 -

Now do this, but string the outputs together in a triangle

        9
       88
      777
     6666
    55555
   444444
  3333333
 22222222
111111111
---------
123456789

# out non-factor sharing numbers

        9
       8#
      7##
     6#66
    5####
   4#4#4#
  3##3##3
 2#2#2#2#
#########

Remove numbers:

        #
       ##
      #
     ####
    # # #
   ## ## 
  # # # #
#########

This would be the output for input 9 (since 9 columns.)

Leading + trailing newlines allowed.

Answer 1

MATL, 17 15 bytes

:Gq:!Zd1=RP35*c

Try it online!

If a leading newline is acceptable: 13 bytes:

:t!Zd1=RP35*c

Explanation

:     % Take input N. Generate row vector [1 2 ... N]
Gq:   % Row vector [1 2 ... N-1].
      % (In the 13-byte version this is replaced by function `t`, which duplicates
      % the array [1 2 ... N])
!     % Transpose into column vector
Zd    % GCD, element-wise with broadcast. Gives (N-1)×N matrix
1=    % True for entries that equal 1, corresponding to relatively prime pairs.
      % The rest of entries are set to false, i.e. 0.
R     % Upper triangular part: set values below diagonal to 0
P     % Flip matrix vertically
35*   % Multiply each entry by 35 (ASCII for '#')
c     % Convert to char. 0 will be displayed as a space. Implicitly display

Answer 2

Jelly, 20 18 bytes

RR⁶”#g’¥?€"Rz⁶U'j⁷

Try it online!

Answer 3

Pyth - 22 bytes

Will try to golf further.

j_.tmsm@"# "n1idkSdSQd

Try it online here.

Answer 4

JavaScript (ES6), 112 bytes

n=>[...s=` `.repeat(n)].map(_=>s.replace(/./g,_=>`# `[+g(n+1,i++)],n-=i=1),g=(i,j)=>i?i>j||g(j%i,i):j>1).join`\n`

Where \n represents the literal newline character. Alternative solution, also 112 bytes:

n=>(s=`# `.repeat(n)).replace(r=/../g,_=>s.replace(r,m=>m[+g(n+1,i++)],n-=i=1)+`
`,g=(i,j)=>i?i>j||g(j%i,i):j>1)

Answer 5

Java, 162 158 bytes

int g(int a,int b){return a<1?b:g(b%a,a);}
String d(int n){String r="";for(int i=0;i<n;i++){for(int j=1;j<=n;)r+=i+j<n|g(n-i,j++)>1?" ":"#";r+="\n";}return r;}

Full program (not updated)

import java.util.Scanner;

public class Q79082 {
    int gcd_ungolfed(int a,int b){
        if(a==0) return b;
        return gcd_ungolfed(b%a,a);
    }
    void draw_ungolfed(int n){
        for(int i=1;i<=n;i++){
            for(int j=1;j<=n;j++){
                if(i+j<=n || gcd_ungolfed(n+1-i,j)!=1){
                    System.out.print(" ");
                }else{
                    System.out.print("#");
                }
            }
            System.out.println();
        }
    }
    int g(int a,int b){return a<1?b:g(b%a,a);}
    String d(int n){String r="";for(int i=0;i<n;i++){for(int j=1;j<=n;j++)r+=(i+j<n||g(n-i,j)>1)?" ":"#";r+="\n";}return r;}
    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        sc.close();
        new Q79082().draw_ungolfed(n);
        System.out.println(new Q79082().d(n));
    }
}

Input/output:

9

        #
       ##
      #  
     ####
    # # #
   ## ## 
  # # # #
#########

        #
       ##
      #  
     ####
    # # #
   ## ## 
  # # # #
#########

Answer 6

SQL (PostGreSQL9.4), 239 291 bytes

Creates a prepared statement that can be executed. I'm sure I can probably take quite a few bytes out of this, but I'll have to pick away at it later. Does a cross join on a range of 1 to n. Calculates the GCD in a lateral join. Where the GCD is 1 and the series A is greater than series B output a '#' otherwise a space. Aggregate the results up into a string grouped by series B.

prepare p(int)as
select string_agg(coalesce(CASE WHEN b<=a AND x=1THEN'#'END,' '),'')from generate_series(1,$1)a,generate_series(1,$1)b,LATERAL(SELECT MAX(G)x FROM generate_series(1,LEAST(a,b))g WHERE a%g+b%g=0)g
group by b
order by b desc

Run in the following way

execute p(13)

string_agg
----------------

            #
           ##
          # #
         ## #
        # # #
       ######
      #   # #
     #### ###
    # # # # #
   ## ## ## #
  # # # # # #
#############

And cleaned up with

deallocate p

Answer 7

Ruby, 84 bytes

->n{s=[];n.times{|i|j=0;m=n-i;s<<(?#*n).gsub(/./){m.gcd(j+=1)>1||m>j ?' ':$&}};s*$/}

Answer 8

Python 2 (120 bytes)

g=lambda m,n:m if n<1 else g(n,m%n)
r=range(input())
for i in r[:0:-1]:print''.join('# '[i>j+1 or g(i,j+1)>1]for j in r)