A327856 The upper left triangular section of square array A091255, read by rows.

1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 3, 1, 5, 1, 2, 3, 2, 3, 6, 1, 1, 1, 1, 1, 1, 7, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 3, 1, 3, 3, 7, 1, 9, 1, 2, 3, 2, 5, 6, 1, 2, 3, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 2, 3, 4, 3, 6, 1, 4, 3, 6, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 2, 1, 2, 1, 2, 7, 2, 7, 2, 1, 2, 1, 14

Offset: 1

Author

Antti Karttunen, Sep 28 2019

Keywords

• nonn
• tabl

Examples

			The triangular table starts as:
  1,
  1, 2,
  1, 1, 3,
  1, 2, 1, 4,
  1, 1, 3, 1, 5,
  1, 2, 3, 2, 3, 6,
  1, 1, 1, 1, 1, 1, 7,
  1, 2, 1, 4, 1, 2, 1, 8,
  1, 1, 3, 1, 3, 3, 7, 1, 9,
  1, 2, 3, 2, 5, 6, 1, 2, 3, 10,
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 rows of triangular table
• Index entries for sequences operating on polynomials in ring GF(2)[X]

Crossrefs

Cf. A000217, A091255.

Programs

PARI

up_to = 105;
A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);
A327856list(up_to) =  { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A091255sq(a,col))); (v); };
v327856 = A327856list(up_to);
A327856(n) = v327856[n];

Formula

A(n,k) = A091255(n,k), with k in range 1 .. n.

a(A000217(n)) = n.