A320675 - OEIS

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

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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