A280170 Primes p such that both 2^(p-1) - 1 and 2^(p+1) - 1 are not squarefree.

19, 41, 79, 101, 109, 137, 139, 199, 271, 281, 311, 379, 401, 439, 461, 499, 521, 601, 619, 641, 701, 727, 739, 761, 769, 811, 821, 859, 881, 919, 941, 953, 1013, 1039, 1061, 1087, 1181, 1279, 1301, 1361, 1399, 1429, 1459, 1481, 1549, 1579, 1601, 1699, 1721, 1759, 1777, 1871, 1879, 1901

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

19 is in this sequence because 2^(19-1) - 1 = 262143 = 3^3*7*19*73 and 2^(19+1) - 1 = 1048575 = 3*5^2*11*31*41.

Mathematica

Select[Prime[Range[200]], ! SquareFreeQ[ 2^(#-1) - 1 ] && ! SquareFreeQ[ 2^(#+1) - 1 ] &] (* Robert Price, Feb 26 2017 *)
Select[Prime[Range[300]], NoneTrue[{2^(#-1)-1, 2^(#+1)-1}, SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 14 2020 *)

Prog

(Magma) [p: p in PrimesUpTo(200) | not IsSquarefree(2^(p-1)-1) and not
IsSquarefree(2^(p+1)-1)];
(PARI) is(n)=isprime(n) && !issquarefree(2^(n-1)-1) && !issquarefree(2^(n+1)-1) \\ Charles R Greathouse IV, Aug 26 2017

Crossrefs

Cf. A013929, A049094, A280149.

Sequence in context: A323391 A248339 A133855 * A262608 A141855 A323387

Adjacent sequences: A280167 A280168 A280169 * A280171 A280172 A280173

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 27 2016

Extensions

Inserted terms 727 and 739 by Robert Price, Feb 26 2017

Added terms a(38)-a(54) by Robert Price, Feb 26 2017

Status

approved