A291691 Primes p such that gpf(lpf(2^p - 1) - 1) = p.

2, 3, 5, 7, 11, 13, 23, 29, 37, 43, 47, 53, 73, 79, 83, 97, 113, 131, 151, 173, 179, 181, 191, 197, 211, 223, 233, 239, 251, 263, 277, 281, 283, 307, 317, 337, 353, 359, 367, 383, 397, 419, 431, 439, 443, 457, 461, 463, 467, 487, 491, 499

Offset

1,1

Comments

This sequence has not been proved to be infinite.

The terms p such that 2^p - 1 is a Mersenne prime are 2, 3, 5, 7, and 13.

If p is prime, then gpf(lpf(2^p - 1) - 1) >= p.

Primes q such that gpf(lpf(2^q - 1) - 1) > q are A292237.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..119

Example

We have gpf(lpf(2^11 - 1) - 1) = gpf(23 - 1) = 11, so 11 is a term.

Mathematica

lpf[n_] := FactorInteger[n][[1, 1]]; gpf[n_] := FactorInteger[n][[-1, 1]]; Select[ Prime@ Range@ 45, gpf[lpf[2^# - 1] - 1] == # &] (* Giovanni Resta, Aug 30 2017 *)

Prog

(PARI) listp(nn) = forprime(p=2, nn, if (vecmax(factor(vecmin(factor(2^p-1)[, 1])-1)[, 1]) == p, print1(p, ", ")); ); \\ Michel Marcus, Aug 30 2017

Crossrefs

Cf. A000040, A000043, A006530, A016047, A020639, A236128.

Contains A002515.

Sequence in context: A229289 A087634 A360932 * A178576 A360147 A038970

Adjacent sequences: A291688 A291689 A291690 * A291692 A291693 A291694

Keyword

nonn

Author

Thomas Ordowski, Aug 30 2017

Extensions

a(17)-a(26) from Michel Marcus, Aug 30 2017

a(27)-a(34) from Giovanni Resta, Aug 30 2017

a(35)-a(52) from Charles R Greathouse IV, Aug 30 2017

Status

approved