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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

%I

%S 1,2,3,7,10,20,27,31,40,127,138,219,245,276,552,650,682,1364,2047,

%T 2728,8191,10922,13515,14043,32747,112347,131071,524287,2796202,

%U 3459945,5592404,7124187,8388607,8530050,10660010,11184808,16645111,17060100,21320020,33554431

%N 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).

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

%C 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.

%C See A320673 for similar sequences.

%e The first terms, alongside their binary representation and the coprime numbers encoded therein, are:

%e n a(n) bin(a(n)) First numbers coprime

%e -- ---- --------- ---------------------

%e 1 1 1 1

%e 2 2 10 1

%e 3 3 11 1, 2

%e 4 7 111 1, 2, 3

%e 5 10 1010 1, 3

%e 6 20 10100 1, 3

%e 7 27 11011 1, 2, 4, 5

%e 8 31 11111 1, 2, 3, 4, 5

%e 9 40 101000 1, 3

%e 10 127 1111111 1, 2, 3, 4, 5, 6, 7

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

%Y Cf. A001348, A070939, A320673.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Oct 19 2018

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Last modified January 25 19:00 EST 2022. Contains 350572 sequences. (Running on oeis4.)