A379007 a(n) = (n^2) XOR ((n^2)-1).

1, 7, 1, 31, 1, 7, 1, 127, 1, 7, 1, 31, 1, 7, 1, 511, 1, 7, 1, 31, 1, 7, 1, 127, 1, 7, 1, 31, 1, 7, 1, 2047, 1, 7, 1, 31, 1, 7, 1, 127, 1, 7, 1, 31, 1, 7, 1, 511, 1, 7, 1, 31, 1, 7, 1, 127, 1, 7, 1, 31, 1, 7, 1, 8191, 1, 7, 1, 31, 1, 7, 1, 127, 1, 7, 1, 31, 1, 7, 1, 511, 1, 7, 1, 31, 1, 7, 1, 127, 1, 7, 1, 31, 1, 7, 1, 2047

Offset: 1

Author

Antti Karttunen, Dec 16 2024

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A000225, A000290, A003987, A007814, A037227, A038712.

Cf. also A283750.

Programs

Mathematica

Map[BitXor[#, # - 1] &, Range[100]^2] (* Paolo Xausa, Dec 18 2024 *)

PARI

A379007(n) = bitxor(n^2, ((n^2)-1));

Python

def A379007(n): return (m:=n**2)^m-1 # Chai Wah Wu, Dec 17 2024

Formula

Multiplicative with a(p^e) = 2^(1+2*e)-1 if p = 2; 1 if p > 2.

a(n) = A038712(A000290(n)).

a(n) = A000225(A037227(n)) = (2^(1+2*A007814(n))) - 1.

Dirichlet g.f.: zeta(s) * (2^s + 2)/(2^s - 4). - Amiram Eldar, Jan 12 2025