OFFSET
1,1
COMMENTS
Odd numbers n > 1 such that gcd(n, 2^(n-1)-1) = 1.
Conjecture: this is a subsequence of A121707. Tested for all terms <= 10^5.
For n > 1, if gcd(n, 2^n-2) = 1, then n is an "anti-Carmichael number" defined: p-1 does not divide n-1 for every prime p dividing n. Generally: for k > 1, gcd(k, b^k-b) = 1 for some integer b if and only if k is an "anti-Carmichael number". - Thomas Ordowski, Aug 14 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A121707(n) for n < 62. A121707(62) = 697 = A306097(1) is the first term of A121707 not in this sequence. - M. F. Hasler, Nov 09 2018
MAPLE
select(n -> igcd(n, 2&^n-2 mod n)=1, [seq(i, i=3..10000, 2)]);
MATHEMATICA
Select[Range[2, 768], GCD[#, 2^# - 2] == 1 &] (* or *)
Select[Range[2, 768], OddQ@ # && GCD[#, 2^(# - 1) - 1] == 1 &] (* Michael De Vlieger, Jan 24 2016 *)
PROG
(PARI) lista(nn) = for(n=2, nn, if(gcd(n, 2^n - 2) == 1, print1(n, ", "))); \\ Altug Alkan, Jan 24 2016
(Magma) [n: n in [2..800] | Gcd(n, 2^n-2) eq 1]; // Vincenzo Librandi, Jan 24 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski and Robert Israel, Jan 24 2016
STATUS
approved