A324350 - OEIS

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

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

OFFSET

0,5

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

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

Adjacent sequences: A324347 A324348 A324349 * A324351 A324352 A324353

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Feb 25 2019

STATUS

approved