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A174275
a(n) = 2^(n-1) mod M(n) where M(n) = A014963(n) is the exponential of the Mangoldt function.
11
0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0
OFFSET
1,1
COMMENTS
Appears to be always either 0 or 1.
This follows from Fermat's Little Theorem. - Charles R Greathouse IV, Feb 13 2011
Characteristic function for odd prime powers (larger than one). - Antti Karttunen, Sep 14 2017, after Charles R Greathouse IV's Feb 13 2011 formula.
FORMULA
a(n) = A000079(n-1) mod A014963(n).
a(n) = 1 if n = p^k for k > 0 and p a prime not equal to 2, a(n) = 0 otherwise. - Charles R Greathouse IV, Feb 13 2011
MATHEMATICA
a[n_] := Mod[2^(n - 1), Exp[MangoldtLambda[n]]] (* Steven Foster Clark, Sep 04 2023 *)
PROG
(PARI) vector(70, n, ispower(k=n, , &k); isprime(k)&k!=2) \\ Charles R Greathouse IV, Feb 13 2011
CROSSREFS
Cf. A062173.
Sequence in context: A144607 A327253 A051840 * A353673 A144599 A144608
KEYWORD
nonn,easy
AUTHOR
Mats Granvik, Mar 14 2010
EXTENSIONS
More terms from Antti Karttunen, Sep 14 2017
Name corrected by Steven Foster Clark, Sep 05 2023
STATUS
approved