A377634 a(n) is the smallest k such that tau(k*2^n - 1) is equal to 2^n where tau = A000005.

2, 4, 17, 130, 1283, 6889, 40037, 638521, 10126943, 186814849, 2092495862

Offset

1,1

Comments

a(12) <= 8167862431, a(13) <= 1052676193433, a(14) <= 30964627320559. - Daniel Suteu, Jan 07 2025

Links

Table of n, a(n) for n=1..11.

Formula

a(n)*2^n - 1 >= A360438(n). - Daniel Suteu, Jan 07 2025

Example

a(1) = 2 because tau(2*2^1 - 1) = tau(4 - 1) = tau(3) = 2 = 2^1;
a(2) = 4 because tau(4*2^2 - 1) = tau(16 - 1) = tau(15) = 4 = 2^2.

Mathematica

a[n_]:=Module[{k=1}, While[DivisorSigma[0, k*2^n-1]!=2^n, k++]; k]; Array[a, 8] (* Stefano Spezia, Dec 29 2024 *)

Prog

(PARI) a(n) = my(k=1); while (numdiv(k*2^n - 1) != 2^n, k++); k; \\ Michel Marcus, Dec 28 2024

Crossrefs

Cf. A000005, A360438.

Sequence in context: A347724 A009323 A307125 * A247260 A048872 A063800

Adjacent sequences: A377631 A377632 A377633 * A377635 A377636 A377637

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Dec 28 2024

Extensions

a(10) from Michel Marcus, Dec 28 2024

a(4) = 17 removed by Vincenzo Librandi, Dec 31 2024

a(5) = 1283 from Vincenzo Librandi, Dec 31 2024

a(11) from Daniel Suteu, Jan 07 2025

Status

approved