A138882 Triangle read by rows: row n lists divisors of n-th even superperfect number A061652(n).

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

Offset: 1

Author

Omar E. Pol, Apr 11 2008

Keywords

• nonn
• tabf

Comments

The number of divisors of n-th even superperfect number is equal to A000043(n), then row n has A000043(n) terms.

The sum of divisors of n-th even superperfect number is equal to n-th Mersenne prime A000668(n), then n-th row sum is equal to A000668(n).

Examples

			Triangle begins:
  1, 2
  1, 2, 4
  1, 2, 4, 8, 16
  1, 2, 4, 8, 16, 32, 64
  1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096
  ...
==============================================================
..... Mersenne ..............................................
....... prime ...............................................
n ... A000668(n) = Sum of divisors of A061652(n) .............
==============================================================
1 ........ 3 ... = 1+2
2 ........ 7 ... = 1+2+4
3 ....... 31 ... = 1+2+4+8+16
4 ...... 127 ... = 1+2+4+8+16+32+64
5 ..... 8191 ... = 1+2+4+8+16+32+64+128+256+512+1024+2048+4096
		

Links

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

Crossrefs

Cf. A000005, A000043, A000203, A000668, A019279, A061652, A133031.

Programs

Mathematica

Flatten[Divisors[2^(MersennePrimeExponent[Range[7]]-1)]] (* Harvey P. Dale, Apr 28 2022 *)