A249917 Square array read by antidiagonals where the n-th row lists the integers x such that gcd(x, sigma(x)) = n.

1, 2, 10, 3, 14, 15, 4, 20, 18, 12, 5, 22, 33, 44, 95, 7, 26, 45, 48, 145, 6, 8, 34, 51, 76, 200, 30, 91, 9, 38, 69, 88, 295, 42, 196, 56, 11, 46, 72, 92, 395, 54, 273, 112, 153, 13, 52, 87, 108, 445, 66, 287, 184, 288, 40, 16, 58, 99, 124, 475, 78, 455, 248, 459, 190, 473

Offset: 1

Author

Michel Marcus, Jan 14 2015

Keywords

• nonn
• tabl

Comments

First line is A014567 and first column is A074391.

This is a permutation of the positive integers.

Examples

			Array begins:
   1,   2,  3,    4,   5,   7,   8, ...
  10,  14,  20,  22,  26,  34,  38, ...
  15,  18,  33,  45,  51,  69,  72, ...
  12,  44,  48,  76,  88,  92, 108, ...
  95, 145, 200, 295, 395, 445, 475, ...
   6,  30,  42,  54,  66,  78, 102, ...
  91, 196, 273, 287, 455, 581, 637, ...
  56, 112, 184, 248, 368, 376, 432, ...
  ...
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A009194 (gcd(n, sigma(n))), A014567 (gcd(n, sigma(n))=1), A074391 (smallest x such that gcd(x, sigma(x)) is n),

Programs

PARI

triangle(nn) = {v = vector(nn); for (n=1, nn, for (k=1, n, if (! v[k], x = 1, x = v[k] + 1); while (gcd(sigma(x), x) != k, x++); print1(x, ", "); v[k] = x;); print(););}