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

Author

Thomas Ordowski and Altug Alkan, Sep 04 2017

Keywords

• nonn

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)

Examples

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

Crossrefs

Cf. A000225, A005420, A006530.

Subsequence of A292199.

Extensions

a(10)-a(41) from Giovanni Resta, Sep 04 2017

a(42)-a(46) from Max Alekseyev, Sep 13 2017