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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
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 (list; graph; refs; listen; history; text; internal format)
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: A100847 A271713 A173132 * A336414 A095010 A295723

Adjacent sequences:  A320672 A320673 A320674 * A320676 A320677 A320678

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Oct 19 2018

STATUS

approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)