A292315 Positive integers not divisible by any number of the form 2^n + 1 for n >= 0.

1, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 121, 127, 131, 133, 137, 139, 143, 149, 151, 157, 161, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 203, 209, 211, 217, 223, 227, 229, 233, 239, 241, 247, 251, 253, 259, 263, 269, 271, 277, 281, 283, 287

Offset: 1

Author

Jeffrey Shallit, Sep 14 2017

Keywords

• nonn

Comments

This is the same as odd numbers not divisible by numbers of the form 2^(2^i) + 1, i >= 0.

Asymptotically, the number of such numbers <= x is x/4 + o(x).

Composite terms are 49, 77, 91, 121, 133, 143, 161, ... - Altug Alkan, Sep 14 2017

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of zeros in A305436.

Programs

Mathematica

Position[Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# - 1] &], {n, 288}], 0][[All, 1]] (* Michael De Vlieger, Jun 11 2018 *)

PARI

list(lim)=my(v=List(),u=[],t); lim\=1; forstep(n=1,lim,[4,2], if(gcd(n,1431655765)==1, listput(v,n))); v=Vec(v); for(i=5,logint(logint(lim-1,2),2), t=2^2^i+1; u=concat(u,t*[1..lim\t])); u=Set(u); setminus(v,u) \\ Charles R Greathouse IV, Sep 14 2017