

A291855


Numbers k such that gpf(2^k  1)  1 is not divisible by k.


2



28, 52, 68, 92, 124, 156, 172, 244, 260, 308, 327, 340, 348, 356, 380, 396, 404, 428, 436, 500, 508, 516, 532, 580, 612, 644, 660, 684, 696, 724, 732, 748, 764, 780, 796, 820, 836, 908, 940, 980, 996, 1056, 1076, 1124, 1172, 1180
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OFFSET

1,1


COMMENTS

For a(n) <= 10^3, all terms are divisible by 4 except 327 = 3*109.
Primes p such that 4*p is a term are 7, 13, 17, 23, 31, 43, 61, ...
From Thomas Ordowski, Sep 04 2017: (Start)
If p == +1 (mod 8) and 2^p  1 is prime, then 4*p is a term.
Conjecture: 4 * A001153(m) for m > 3 is a subsequence.
Primes q such that q1 is a term are 29, 53, 157, 173, 349, 397, ... (End)


LINKS

Table of n, a(n) for n=1..46.


EXAMPLE

28 is a term because gpf(2^28  1) == 15 (mod 28).


CROSSREFS

Cf. A000225, A005420, A006530.
Subsequence of A292199.
Sequence in context: A161923 A309145 A039772 * A181792 A181793 A224545
Adjacent sequences: A291852 A291853 A291854 * A291856 A291857 A291858


KEYWORD

nonn


AUTHOR

Thomas Ordowski and Altug Alkan, Sep 04 2017


EXTENSIONS

a(10)a(41) from Giovanni Resta, Sep 04 2017
a(42)a(46) from Max Alekseyev, Sep 13 2017


STATUS

approved



