A355330 Numbers k such that A020696(2^k-1) < A020696(2^k+1).

1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 41, 45, 46, 47, 49, 51, 53, 57, 59, 61, 62, 65, 67, 69, 71, 73, 77, 78, 81, 83, 85, 89, 91, 93, 95, 97, 98, 99, 101, 103, 105, 107, 109, 111, 113, 115, 118, 121, 122, 123, 125

Offset

1,2

Comments

Sándor (2021) showed that all the Mersenne exponents (A000043) are in this sequence and conjectured that both this sequence and its complement are infinite.

Links

Table of n, a(n) for n=1..64.

József Sándor, On Vandiver's arithmetical function - I, Notes on Number Theory and Discrete Mathematics, Vol. 27, No. 3 (2021), pp. 29-38.

Example

2 is a term since A020696(2^2-1) = A020696(3) = 8 and A020696(2^2+1) = A020696(5) = 12 > 8.

Mathematica

v[n_] := Times @@ (Divisors[n] + 1); Select[Range[150], v[2^# - 1] < v[2^# + 1] &]

Prog

(PARI) f(n) = my(d = divisors(n)); prod(i=1, #d, d[i]+1); \\ A020696
isok(k) = f(2^k-1) < f(2^k+1); \\ Michel Marcus, Jun 30 2022

Crossrefs

Cf. A000043, A000668, A020696.

Sequence in context: A258037 A186330 A153809 * A338923 A360126 A004274

Adjacent sequences: A355327 A355328 A355329 * A355331 A355332 A355333

Keyword

nonn

Author

Amiram Eldar, Jun 29 2022

Status

approved