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A139247
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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).
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2
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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Table of n, a(n) for n=1..36.
O. E. Pol, Determinacion geometrica de los numeros primos y perfectos".
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EXAMPLE
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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
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CROSSREFS
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Cf. A000043, A000396, A000668, A018254, A018487, A133024, A133025, A133031, A133049, A135652, A135653, A135654, A135655.
Sequence in context: A138218 A056055 A070523 * A124611 A043305 A192124
Adjacent sequences: A139244 A139245 A139246 * A139248 A139249 A139250
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KEYWORD
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nonn,tabf
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AUTHOR
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Omar E. Pol, Apr 22 2008
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STATUS
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approved
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