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A233757 Triangle read by rows: T(n,k) = (2^n-1)*2^(k-1), for n >= 1 and 1<=k<=n.

%I A233757 #20 Oct 10 2018 20:22:09
%S A233757 1,3,6,7,14,28,15,30,60,120,31,62,124,248,496,63,126,252,504,1008,
%T A233757 2016,127,254,508,1016,2032,4064,8128,255,510,1020,2040,4080,8160,
%U A233757 16320,32640,511,1022,2044,4088,8176,16352,32704,65408,130816,1023,2046,4092
%N A233757 Triangle read by rows: T(n,k) = (2^n-1)*2^(k-1), for n >= 1 and 1<=k<=n.
%C A233757 Column 1 gives the positive terms of A000225.
%C A233757 Leading diagonal gives the positive terms of A006516.
%C A233757 The sum of row n is T(n,1)^2 = A000225(n)^2, hence row sums give A060867.
%C A233757 If n = A000043(m) then T(n,1) = A000668(m) and row n lists last n divisors of m-th even perfect number, which are also the divisors that are multiples of m-th Mersenne prime, for m >= 1.
%C A233757 If n = A000043(m) then T(n,n) = A000396(m), assuming there are no odd perfect numbers, for m >= 1.
%H A233757 Harvey P. Dale, <a href="/A233757/b233757.txt">Table of n, a(n) for n = 1..5000</a>
%F A233757 T(n,k) = A000225(n)*A000079(k-1), n >= 1, 1<=k<=n.
%e A233757 Triangle begins:
%e A233757 1;
%e A233757 3, 6;
%e A233757 7, 14, 28;
%e A233757 15, 30, 60, 120;
%e A233757 31, 62, 124, 248, 496;
%e A233757 63, 126, 252, 504, 1008, 2016;
%e A233757 127, 254, 508, 1016, 2032, 4064, 8128;
%e A233757 255, 510, 1020, 2040, 4080, 8160, 16320, 32640;
%e A233757 511, 1022, 2044, 4088, 8176, 16352, 32704, 65408, 130816;
%e A233757 ...
%t A233757 Table[(2^n-1)2^(k-1),{n,10},{k,n}]//Flatten (* _Harvey P. Dale_, Oct 10 2018 *)
%Y A233757 Cf. A000043, A000079, A000225, A000396, A000668, A006516, A018254, A018487, A059268, A060867, A133024, A133025, A135652-A135655, A139247.
%K A233757 nonn,tabl
%O A233757 1,2
%A A233757 _Omar E. Pol_, Jan 12 2014