A263647 -id:A263647 - cp's OEIS frontend

A272475 Numbers n such that 2^n-1 and 3^n-1 are not coprime.

4, 6, 8, 10, 11, 12, 16, 18, 20, 22, 23, 24, 28, 30, 32, 33, 35, 36, 40, 42, 43, 44, 46, 48, 50, 52, 54, 55, 56, 58, 60, 64, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 82, 83, 84, 86, 88, 90, 92, 95, 96, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 117

Offset: 1

Vincenzo Librandi, May 01 2016

nonn

Complement of A263647.

			gcd(2^4-1, 3^4-1) = gcd(15,80) = 5, so a(1) = 4.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A263647.

[n: n in [1..200] | not Gcd(2^n-1, 3^n-1) eq 1];

Select[Range[200], ! GCD[2^# - 1, 3^# - 1] == 1 &]

isok(n) = gcd(2^n-1, 3^n-1) != 1; \\ Michel Marcus, May 01 2016

A265166 Numbers n such that 2^n-1 and 5^n-1 are coprime.

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 37, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 97, 101, 103, 107, 109, 111, 113, 115, 121, 123, 125, 127, 129, 131, 133, 137, 139, 141, 143

Offset: 1

Vincenzo Librandi, May 01 2016

nonn

Also numbers n such that A270390(n) = 1.

Conjectured to be infinite: see the Ailon and Rudnick paper.

			gcd(2^1-1, 5^1-1) = gcd(1,4) = 1, so a(1) = 1.
gcd(2^3-1, 5^3-1) = gcd(7,124) = 1, so a(2) = 3.
gcd(2^4-1, 5^4-1) = gcd(15,624) = 3, so 4 is not in the sequence.

N. Ailon and Z. Rudnick, Torsion points on curves and common divisors of a^k - 1 and b^k - 1 , Acta Arith. 113 (2004), pp. 31-38.

Cf. A000225, A024049, A263647, A270390.

[n: n in [1..200] | Gcd(2^n-1,5^n-1) eq 1];

Select[Range[200], GCD[2^# - 1, 5^# - 1] == 1 &]
Select[Range[150],CoprimeQ[2^#-1,5^#-1]&] (* Harvey P. Dale, Apr 12 2018 *)

cp's OEIS Frontend

A272475 Numbers n such that 2^n-1 and 3^n-1 are not coprime.

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