A351961 Square array A(n,k) = A156552(gcd(A005940(1+n), A005940(1+k))), read by antidiagonals.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 2, 1, 4, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 5, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 6, 1, 0, 1, 2, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 4, 0, 2, 0, 0

Offset: 0

Author

Antti Karttunen, Feb 26 2022

Keywords

• nonn
• tabl

Comments

The indices run as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), etc. The array is symmetric.

Examples

			The top left corner of the array:
   n=  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17
-----|--------------------------------------------------------------
k= 0 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0,  0,  0,
   1 | 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,  0,  1,  0,  1,  0,  1,  0,  1,
   2 | 0, 0, 2, 0, 0, 2, 2, 0, 0, 0,  2,  2,  0,  2,  2,  0,  0,  0,
   3 | 0, 1, 0, 3, 0, 1, 0, 3, 0, 1,  0,  3,  0,  1,  0,  3,  0,  1,
   4 | 0, 0, 0, 0, 4, 0, 0, 0, 0, 4,  4,  0,  4,  0,  0,  0,  0,  0,
   5 | 0, 1, 2, 1, 0, 5, 2, 1, 0, 1,  2,  5,  0,  5,  2,  1,  0,  1,
   6 | 0, 0, 2, 0, 0, 2, 6, 0, 0, 0,  2,  2,  0,  6,  6,  0,  0,  0,
   7 | 0, 1, 0, 3, 0, 1, 0, 7, 0, 1,  0,  3,  0,  1,  0,  7,  0,  1,
   8 | 0, 0, 0, 0, 0, 0, 0, 0, 8, 0,  0,  0,  0,  0,  0,  0,  0,  8,
   9 | 0, 1, 0, 1, 4, 1, 0, 1, 0, 9,  4,  1,  4,  1,  0,  1,  0,  1,
  10 | 0, 0, 2, 0, 4, 2, 2, 0, 0, 4, 10,  2,  4,  2,  2,  0,  0,  0,
  11 | 0, 1, 2, 3, 0, 5, 2, 3, 0, 1,  2, 11,  0,  5,  2,  3,  0,  1,
  12 | 0, 0, 0, 0, 4, 0, 0, 0, 0, 4,  4,  0, 12,  0,  0,  0,  0,  0,
  13 | 0, 1, 2, 1, 0, 5, 6, 1, 0, 1,  2,  5,  0, 13,  6,  1,  0,  1,
  14 | 0, 0, 2, 0, 0, 2, 6, 0, 0, 0,  2,  2,  0,  6, 14,  0,  0,  0,
  15 | 0, 1, 0, 3, 0, 1, 0, 7, 0, 1,  0,  3,  0,  1,  0, 15,  0,  1,
  16 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,  0,  0,  0,  0,  0,  0, 16,  0,
  17 | 0, 1, 0, 1, 0, 1, 0, 1, 8, 1,  0,  1,  0,  1,  0,  1,  0, 17,
		

Links

• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A003989, A005940, A156552.

Cf. A001477 (main diagonal).

Cf. also A341520, A351960, A351962.

Programs

PARI

up_to = 104; \\ 10439 = binomial(144+1,2)-1
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A351961sq(n,k) = A156552(gcd(A005940(1+n),A005940(1+k)));
A351961list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0,oo, for(col=0,a, i++; if(i > #v, return(v)); v[i] = A351961sq(col,(a-(col))))); (v); };
v351961 = A351961list(up_to);
A351961(n) = v351961[1+n];

Formula

For all x, y >= 0, A(x, y) = A(x, A351960(x,y)) = A(A351960(x,y), y).