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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.
12

%I #34 Oct 20 2024 17:42:33

%S 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,

%T 7,73,511,1,3,11,31,33,93,341,1023,1,23,89,2047,1,3,5,7,9,13,15,21,35,

%U 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

%N 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.

%H Seiichi Manyama, <a href="/A361438/b361438.txt">Rows n = 1..64, flattened</a>

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%e Triangle begins:

%e 1;

%e 1, 3;

%e 1, 7;

%e 1, 3, 5, 15;

%e 1, 31;

%e 1, 3, 7, 9, 21, 63;

%e 1, 127;

%e 1, 3, 5, 15, 17, 51, 85, 255;

%e 1, 7, 73, 511;

%e 1, 3, 11, 31, 33, 93, 341, 1023;

%e 1, 23, 89, 2047;

%p T:= n-> sort([numtheory[divisors](2^n-1)[]])[]:

%p seq(T(n), n=1..12); # _Alois P. Heinz_, Oct 20 2024

%t Divisors[2^Range[15] - 1] (* _Paolo Xausa_, Jul 02 2024 *)

%Y Subsequence of A027750.

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

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

%K nonn,tabf,look

%O 1,3

%A _Seiichi Manyama_, Mar 12 2023