A135655 -id:A135655 - cp's OEIS frontend

A139248 Triangle read by rows: row n lists the proper divisors of n-th even superperfect number A061652(n).

1, 1, 2, 1, 2, 4, 8, 1, 2, 4, 8, 16, 32, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 1, 2, 4, 8, 16

Offset: 1

Omar E. Pol, Apr 22 2008

Also, row n list the proper divisors of n-th superperfect number A019279(n), if there are no odd superperfect numbers.

Row n has A000043(n) - 1 = A090748(n) terms.

			Triangle begins:
  1
  1, 2
  1, 2, 4, 8
  1, 2, 4, 8, 16, 32
  1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048
  1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768
  ...

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

Cf. A000043, A000668, A018254, A018487, A019279, A061652, A090748, A133024, A133025, A133031, A133049, A135652, A135653, A135654, A135655, A139246.

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

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Jan 12 2014

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.

			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;
...

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

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

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

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

cp's OEIS Frontend

A139248 Triangle read by rows: row n lists the proper divisors of n-th even superperfect number A061652(n).

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