A138882 - OEIS

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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

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OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..62.

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A300653 A256009 A123937 * A074634 A152036 A035015

Adjacent sequences: A138879 A138880 A138881 * A138883 A138884 A138885

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 11 2008

STATUS

approved