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

1,2

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.

Links

Table of n, a(n) for n=1..40.

Example

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

Prog

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

Crossrefs

Cf. A001348, A070939, A320673.

Sequence in context: A356364 A173132 A351704 * A336414 A095010 A295723

Adjacent sequences: A320672 A320673 A320674 * A320676 A320677 A320678

Keyword

nonn,base

Author

Rémy Sigrist, Oct 19 2018

Status

approved