A324350 Square array read by antidiagonals: A(x,y) = gcd(A276086(x),A276086(y)), for x, y >= 0.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 3, 3, 1, 1, 1, 2, 3, 6, 3, 2, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 2, 1, 6, 9, 6, 1, 2, 1, 1, 1, 1, 1, 9, 9, 1, 1, 1, 1, 1, 2, 3, 2, 1, 18, 1, 2, 3, 2, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 2, 3, 6, 3, 2, 5, 2, 3, 6, 3, 2, 1, 1, 1, 3, 3, 3, 3, 5, 5, 3, 3, 3, 3, 1, 1, 1, 2, 1, 6, 9, 6, 5, 10, 5, 6, 9, 6, 1, 2, 1

Offset: 0

Author

Antti Karttunen, Feb 25 2019

Keywords

• nonn
• tabl

Examples

			The array A begins:
       0   1   2   3   4   5   6   7   8   9  10  11  12
  x/y  ------------------------------------------------------
   0:  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
   1:  1,  2,  1,  2,  1,  2,  1,  2,  1,  2,  1,  2,  1, ...
   2:  1,  1,  3,  3,  3,  3,  1,  1,  3,  3,  3,  3,  1, ...
   3:  1,  2,  3,  6,  3,  6,  1,  2,  3,  6,  3,  6,  1, ...
   4:  1,  1,  3,  3,  9,  9,  1,  1,  3,  3,  9,  9,  1, ...
   5:  1,  2,  3,  6,  9, 18,  1,  2,  3,  6,  9, 18,  1, ...
   6:  1,  1,  1,  1,  1,  1,  5,  5,  5,  5,  5,  5,  5, ...
   7:  1,  2,  1,  2,  1,  2,  5, 10,  5, 10,  5, 10,  5, ...
   8:  1,  1,  3,  3,  3,  3,  5,  5, 15, 15, 15, 15,  5, ...
   9:  1,  2,  3,  6,  3,  6,  5, 10, 15, 30, 15, 30,  5, ...
  10:  1,  1,  3,  3,  9,  9,  5,  5, 15, 15, 45, 45,  5, ...
  11:  1,  2,  3,  6,  9, 18,  5, 10, 15, 30, 45, 90,  5, ...
  12:  1,  1,  1,  1,  1,  1,  5,  5,  5,  5,  5,  5, 25, ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..7259 (the first 120 antidiagonals of the array)
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65702
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003989, A276086 (central diagonal), A324198, A324351.

Programs

PARI

up_to = 65703; \\ = binomial(362+1,2)
A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
A324350sq(row,col) = gcd(A276086(row),A276086(col));
A324350list(up_to) = { my(v = vector(up_to), i=0); for(a=0,oo, for(col=0,a, if(i++ > up_to, return(v)); v[i] = A324350sq(a-col,col))); (v); };
v324350 = A324350list(up_to);
A324350(n) = v324350[1+n];

Formula

A(x,y) = gcd(A276086(x), A276086(y)).

A(x,y) = A276086(A324351(x,y)).