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A139247 Triangle read by rows: row n lists the divisors of n-th perfect number A000396(n) that are multiples of n-th Mersenne prime A000668(n). 3
3, 6, 7, 14, 28, 31, 62, 124, 248, 496, 127, 254, 508, 1016, 2032, 4064, 8128, 8191, 16382, 32764, 65528, 131056, 262112, 524224, 1048448, 2096896, 4193792, 8387584, 16775168, 33550336, 131071, 262142, 524284, 1048568, 2097136, 4193792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, row n list the divisors of n-th perfect number that are not powers of 2.

First term of row n is the n-th Mersenne prime A000668(n). Last term of row n is the n-th perfect number A000396(n). Row n has A000043(n) terms. The sum of row n is equal to A133049(n), the square of n-th Mersenne prime A000668(n).

LINKS

Table of n, a(n) for n=1..36.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos".

EXAMPLE

Triangle begins:

3, 6,

7, 14, 28

31, 62, 124, 248, 496

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

==========================================================

Row .... First term ..... Last term ....... Row sum ......

n ..... (A000668(n)) ... (A000396(n)) ... (A000668(n)^2) .

==========================================================

1 ............ 3 .............. 6 ......... 3^2 = 9

2 ............ 7 ............. 28 ......... 7^2 = 49

3 ........... 31 ............ 496 ........ 31^2 = 961

4 .......... 127 ........... 8128 ....... 127^2 = 16129

5 ......... 8191 ....... 33550336 ...... 8191^2 = 67092481

CROSSREFS

Cf. A000043, A000396, A000668, A018254, A018487, A133024, A133025, A133031, A133049, A135652, A135653, A135654, A135655.

Sequence in context: A056055 A070523 A233757 * A124611 A281900 A266615

Adjacent sequences:  A139244 A139245 A139246 * A139248 A139249 A139250

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 22 2008

STATUS

approved

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Last modified February 23 05:44 EST 2018. Contains 299473 sequences. (Running on oeis4.)