A291855 Numbers k such that gpf(2^k - 1) - 1 is not divisible by k.

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

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 q-1 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