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

1,1

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

Prog

(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

Crossrefs

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

Cf. A067874 (subsequence).

Sequence in context: A209211 A064676 A147819 * A230201 A373787 A059534

Adjacent sequences: A379962 A379963 A379964 * A379966 A379967 A379968

Keyword

nonn

Author

Antti Karttunen, Jan 24 2025

Status

approved