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URL: https://oeis.org/A379007

⇱ A379007 - OEIS

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A379007
a(n) = (n^2) XOR ((n^2)-1).
3
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
1,2
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
MATHEMATICA
Map[BitXor[#, # - 1] &, Range[100]^2] (* Paolo Xausa, Dec 18 2024 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Dec 16 2024
STATUS
approved