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
Keywords
Examples
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.
Programs
-
Magma
[p: p in PrimesUpTo(200) | not IsSquarefree(2^(p-1)-1) and not IsSquarefree(2^(p+1)-1)];
-
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 *)
-
PARI
is(n)=isprime(n) && !issquarefree(2^(n-1)-1) && !issquarefree(2^(n+1)-1) \\ Charles R Greathouse IV, Aug 26 2017
Extensions
Inserted terms 727 and 739 by Robert Price, Feb 26 2017
Added terms a(38)-a(54) by Robert Price, Feb 26 2017