A361438 -id:A361438 - cp's OEIS frontend

A075708 Sum of the divisors of 2^n - 1.

1, 4, 8, 24, 32, 104, 128, 432, 592, 1536, 2160, 8736, 8192, 22528, 38912, 111456, 131072, 473600, 524288, 1999872, 2466048, 5909760, 8567136, 38054016, 34713728, 89522176, 155493536, 462274560, 539922240, 2015330304, 2147483648

Offset: 1

Joseph L. Pe, Oct 03 2002

nonn

The set {a(n)/(2^n-1)} is dense in [1, oo) (Luca, 2003). - Amiram Eldar, Mar 04 2021

Amiram Eldar, Table of n, a(n) for n = 1..1206
Paul Erdős, On the sum Sigma_{d|2^n-1} d^{-1}, Israel Journal of Mathematics, Vol. 9. No. 1 (1971), pp. 43-48; alternative link.
Vaclav Kotesovec, Plot of a(n)/((2^n-1)*log(log(n))) for n = 1..1200
Florian Luca, On the sum of divisors of the Mersenne numbers, Mathematica Slovaca, Vol. 53. No. 5 (2003), pp. 457-466.

Cf. A000203, A000225.
A247938 is a subsequence.
Row sums of A361438.

Table[DivisorSigma[1, 2^n - 1], {n, 1, 40}]

a(n)=sigma(2^n-1) \\ Charles R Greathouse IV, Feb 04 2013

a(n) = sigma(2^n - 1).
a(n) = A000203(A000225(n)). - Omar E. Pol, Dec 08 2019
a(n)/(2^n-1) < c * log(log(n)), where c > 0 is a constant (Erdős, 1971). - Amiram Eldar, Mar 04 2021

A374237 Irregular triangle read by rows where row n lists, in increasing order, the divisors of 2^n + 1.

Original entry on oeis.org

1, 2, 1, 3, 1, 5, 1, 3, 9, 1, 17, 1, 3, 11, 33, 1, 5, 13, 65, 1, 3, 43, 129, 1, 257, 1, 3, 9, 19, 27, 57, 171, 513, 1, 5, 25, 41, 205, 1025, 1, 3, 683, 2049, 1, 17, 241, 4097, 1, 3, 2731, 8193, 1, 5, 29, 113, 145, 565, 3277, 16385, 1, 3, 9, 11, 33, 99, 331, 993, 2979, 3641, 10923, 32769

Offset: 0

Paolo Xausa, Jul 02 2024

			Triangle begins:
   [0]  1,   2;
   [1]  1,   3;
   [2]  1,   5;
   [3]  1,   3,  9;
   [4]  1,  17;
   [5]  1,   3, 11,  33;
   [6]  1,   5, 13,  65;
   [7]  1,   3, 43, 129;
   [8]  1, 257;
   [9]  1,   3,  9,  19,  27,   57, 171, 513;
  [10]  1,   5, 25,  41, 205, 1025;
  ...

Paolo Xausa, Table of n, a(n) for n = 0..11484 (rows 0..135 of the triangle, flattened).
Index entries for sequences related to divisors of numbers

Subsequence of A027750.
Cf. A000051, A002586 (2nd column), A046798 (row lengths), A069060 (row products), A069061 (row sums).
Cf. A361438 (analogous for 2^n - 1).

T:= n-> sort([numtheory[divisors](2^n+1)[]])[]:
seq(T(n), n=0..15);  # Alois P. Heinz, Oct 20 2024

Mathematica
```
Divisors[2^Range[0, 20] + 1]
```

A003546 Divisors of 2^40 - 1.

Original entry on oeis.org

1, 3, 5, 11, 15, 17, 25, 31, 33, 41, 51, 55, 75, 85, 93, 123, 155, 165, 187, 205, 255, 275, 341, 425, 451, 465, 527, 561, 615, 697, 775, 825, 935, 1023, 1025, 1271, 1275, 1353, 1581, 1705, 2091, 2255, 2325

Offset: 1

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 1..192 (all divisors)
Index entries for sequences related to divisors of numbers

Row n = 40 of A361438.

Divisors[2^40 - 1] (* Paolo Xausa, Jul 02 2024 *)

divisors(2^40-1) \\ Charles R Greathouse IV, Jun 21 2017

A003554 Divisors of 2^50 - 1.

Original entry on oeis.org

1, 3, 11, 31, 33, 93, 251, 341, 601, 753, 1023, 1801, 1803, 2761, 4051, 5403, 6611, 7781, 8283, 12153, 18631, 19811, 19833, 23343, 44561, 55831, 55893, 59433, 85591, 125581, 133683, 150851, 167493, 204941

Offset: 1

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 1..128 (all divisors)
Index entries for sequences related to divisors of numbers

Row n = 50 of A361438.

Divisors[2^50 - 1] (* Paolo Xausa, Jul 02 2024 *)

divisors(2^50 - 1) \\ Charles R Greathouse IV, Jul 10 2016

A003527 Divisors of 2^16 - 1.

Original entry on oeis.org

1, 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535

Offset: 1

N. J. A. Sloane

Subset of A004729 because 2^32 - 1 = (2^16 + 1)*(2^16 - 1). - R. J. Mathar, May 24 2008

Index entries for sequences related to divisors of numbers

First entries of A001317.

Row n = 16 of A361438.

Divisors[2^16 - 1] (* Paolo Xausa, Jul 01 2024 *)

divisors(2^16-1) \\ Charles R Greathouse IV, Jun 21 2017

A003530 Divisors of 2^21 - 1.

Original entry on oeis.org

1, 7, 49, 127, 337, 889, 2359, 6223, 16513, 42799, 299593, 2097151

Offset: 1

N. J. A. Sloane

Index entries for sequences related to divisors of numbers

Row n = 21 of A361438.

Divisors[2^21 - 1] (* Paolo Xausa, Jul 02 2024 *)

divisors(2^21-1) \\ Charles R Greathouse IV, Jun 21 2017

A003550 Divisors of 2^45 - 1.

Original entry on oeis.org

1, 7, 31, 73, 151, 217, 511, 631, 1057, 2263, 4417, 4681, 11023, 15841, 19561, 23311, 32767, 46063, 77161, 95281, 136927, 163177, 322441, 341713, 666967, 722641, 1427953, 1701703, 2391991, 2953711, 3519961

Offset: 1

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 1..64 (all divisors)
Index entries for sequences related to divisors of numbers

Row n = 45 of A361438.

Divisors[2^45 - 1] (* Paolo Xausa, Jul 02 2024 *)

divisors(2^45-1) \\ Charles R Greathouse IV, Jun 21 2017

A003526 Divisors of 2^15 - 1.

Original entry on oeis.org

1, 7, 31, 151, 217, 1057, 4681, 32767

Offset: 1

N. J. A. Sloane

Index entries for sequences related to divisors of numbers

Row n = 15 of A361438.

Divisors[2^15 - 1] (* Paolo Xausa, Jul 02 2024 *)

divisors(2^15-1) \\ Charles R Greathouse IV, Jun 22 2017

A003534 Divisors of 2^26 - 1.

Original entry on oeis.org

1, 3, 2731, 8191, 8193, 24573, 22369621, 67108863

Offset: 1

N. J. A. Sloane

Index entries for sequences related to divisors of numbers

Row n = 26 of A361438.

Divisors[2^26 - 1] (* Paolo Xausa, Jul 02 2024 *)

divisors(2^26-1) \\ Charles R Greathouse IV, Jun 22 2017

A003541 Divisors of 2^34 - 1.

Original entry on oeis.org

1, 3, 43691, 131071, 131073, 393213, 5726623061, 17179869183

Offset: 1

N. J. A. Sloane

Index entries for sequences related to divisors of numbers

Row n = 34 of A361438.

Divisors[2^34 - 1] (* Paolo Xausa, Jul 02 2024 *)

divisors(2^34-1) \\ Charles R Greathouse IV, Jun 22 2017

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A075708 Sum of the divisors of 2^n - 1.

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A374237 Irregular triangle read by rows where row n lists, in increasing order, the divisors of 2^n + 1.

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A003546 Divisors of 2^40 - 1.

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A003554 Divisors of 2^50 - 1.

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A003527 Divisors of 2^16 - 1.

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A003530 Divisors of 2^21 - 1.

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A003550 Divisors of 2^45 - 1.

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A003526 Divisors of 2^15 - 1.

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A003534 Divisors of 2^26 - 1.

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