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A324350
Square array read by antidiagonals: A(x,y) = gcd(A276086(x),A276086(y)), for x, y >= 0.
5
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
0,5
FORMULA
A(x,y) = gcd(A276086(x), A276086(y)).
A(x,y) = A276086(A324351(x,y)).
EXAMPLE
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, ...
PROG
(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];
CROSSREFS
Cf. A003989, A276086 (central diagonal), A324198, A324351.
Sequence in context: A003989 A091255 A332013 * A175466 A214403 A261527
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Feb 25 2019
STATUS
approved