A320675 Positive integers m with binary expansion (b_1, ..., b_k) (where k = A070939(m)) such that b_i = [gcd(m, i)=1] for i = 1..k (where [] is an Iverson bracket).

1, 2, 3, 7, 10, 20, 27, 31, 40, 127, 138, 219, 245, 276, 552, 650, 682, 1364, 2047, 2728, 8191, 10922, 13515, 14043, 32747, 112347, 131071, 524287, 2796202, 3459945, 5592404, 7124187, 8388607, 8530050, 10660010, 11184808, 16645111, 17060100, 21320020, 33554431

Offset: 1

Author

Rémy Sigrist, Oct 19 2018

Keywords

• nonn
• base

Comments

In other words, the ones in the binary representation of a term of this sequence encode the first numbers coprime to this term.

This sequence contains every term of A001348: 2^2 - 1 belongs to this sequence, and for any odd prime number p, if q divides 2^p - 1, then q > p and gcd(p, i) = 1 for i = 1..p.

See A320673 for similar sequences.

Examples

			The first terms, alongside their binary representation and the coprime numbers encoded therein, are:
  n   a(n)  bin(a(n))  First numbers coprime
  --  ----  ---------  ---------------------
   1     1  1          1
   2     2  10         1
   3     3  11         1, 2
   4     7  111        1, 2, 3
   5    10  1010       1, 3
   6    20  10100      1, 3
   7    27  11011      1, 2, 4, 5
   8    31  11111      1, 2, 3, 4, 5
   9    40  101000     1, 3
  10   127  1111111    1, 2, 3, 4, 5, 6, 7
		

Crossrefs

Cf. A001348, A070939, A320673.

Programs

PARI

is(n) = my (b=binary(n)); b==vector(#b, k, gcd(n, k)==1)