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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)