A379965 Numbers k such that (k^2)-1 is not divisible by p^p for any prime p.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160

Offset: 1

Author

Antti Karttunen, Jan 24 2025

Keywords

• nonn

Comments

Numbers k for which (k^2)-1 is in A048103.

Even numbers k such that both k-1 and k+1 are in A048103.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A048103, A379964 (characteristic function), A379963.

Cf. A067874 (subsequence).

Programs

PARI

is_A379965 = A379964;

Python

from itertools import count, islice
from sympy import factorint
def A379965_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:all(p>e for p,e in factorint(n-1).items()) and all(p>e for p,e in factorint(n+1).items()),count((m:=max(startvalue,1))+(m&1),2))
A379965_list = list(islice(A379965_gen(),30)) # Chai Wah Wu, Jan 24 2025