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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. 1
1, 3, 6, 7, 14, 28, 15, 30, 60, 120, 31, 62, 124, 248, 496, 63, 126, 252, 504, 1008, 2016, 127, 254, 508, 1016, 2032, 4064, 8128, 255, 510, 1020, 2040, 4080, 8160, 16320, 32640, 511, 1022, 2044, 4088, 8176, 16352, 32704, 65408, 130816, 1023, 2046, 4092 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 1 gives the positive terms of A000225.

Leading diagonal gives the positive terms of A006516.

The sum of row n is T(n,1)^2 = A000225(n)^2, hence row sums give A060867.

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.

If n = A000043(m) then T(n,n) = A000396(m), assuming there are no odd perfect numbers, for m >= 1.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..5000

FORMULA

T(n,k) = A000225(n)*A000079(k-1), n >= 1, 1<=k<=n.

EXAMPLE

Triangle begins:

1;

3, 6;

7, 14, 28;

15, 30, 60, 120;

31, 62, 124, 248, 496;

63, 126, 252, 504, 1008, 2016;

127, 254, 508, 1016, 2032, 4064, 8128;

255, 510, 1020, 2040, 4080, 8160, 16320, 32640;

511, 1022, 2044, 4088, 8176, 16352, 32704, 65408, 130816;

...

MATHEMATICA

Table[(2^n-1)2^(k-1), {n, 10}, {k, n}]//Flatten (* Harvey P. Dale, Oct 10 2018 *)

CROSSREFS

Cf. A000043, A000079, A000225, A000396, A000668, A006516, A018254, A018487, A059268, A060867, A133024, A133025, A135652-A135655, A139247.

Sequence in context: A070523 A350277 A350278 * A341622 A139247 A124611

Adjacent sequences:  A233754 A233755 A233756 * A233758 A233759 A233760

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Jan 12 2014

STATUS

approved

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Last modified August 16 12:15 EDT 2022. Contains 356168 sequences. (Running on oeis4.)