A361438 Triangle T(n,k), n >= 1, 1 <= k <= A046801(n), read by rows, where T(n,k) is k-th smallest divisor of 2^n-1.

1, 1, 3, 1, 7, 1, 3, 5, 15, 1, 31, 1, 3, 7, 9, 21, 63, 1, 127, 1, 3, 5, 15, 17, 51, 85, 255, 1, 7, 73, 511, 1, 3, 11, 31, 33, 93, 341, 1023, 1, 23, 89, 2047, 1, 3, 5, 7, 9, 13, 15, 21, 35, 39, 45, 63, 65, 91, 105, 117, 195, 273, 315, 455, 585, 819, 1365, 4095, 1, 8191, 1, 3, 43, 127, 129, 381, 5461, 16383

Offset: 1

Author

Seiichi Manyama, Mar 12 2023

Keywords

• nonn
• tabf
• look

Examples

			Triangle begins:
  1;
  1,   3;
  1,   7;
  1,   3,  5,   15;
  1,  31;
  1,   3,  7,    9, 21, 63;
  1, 127;
  1,   3,  5,   15, 17, 51,  85,  255;
  1,   7, 73,  511;
  1,   3, 11,   31, 33, 93, 341, 1023;
  1,  23, 89, 2047;
		

Links

• Seiichi Manyama, Rows n = 1..64, flattened
• Index entries for sequences related to divisors of numbers

Crossrefs

Subsequence of A027750.

Cf. A000225, A049479 (2nd column), A075708 (row sums).

Cf. A374237 (analogous for 2^n + 1).

Programs

Maple

T:= n-> sort([numtheory[divisors](2^n-1)[]])[]:
seq(T(n), n=1..12);  # Alois P. Heinz, Oct 20 2024

Mathematica

Divisors[2^Range[15] - 1] (* Paolo Xausa, Jul 02 2024 *)