A174275 a(n) = 2^(n-1) mod M(n) where M(n) = A014963(n) is the exponential of the Mangoldt function.

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

Author

Mats Granvik, Mar 14 2010

Keywords

• nonn
• easy

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16385
• Index entries for characteristic functions

Crossrefs

Cf. A062173.

Programs

Mathematica

a[n_] := Mod[2^(n - 1), Exp[MangoldtLambda[n]]] (* Steven Foster Clark, Sep 04 2023 *)

PARI

vector(70, n, ispower(k=n, , &k); isprime(k)&k!=2) \\ Charles R Greathouse IV, Feb 13 2011

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

Extensions

More terms from Antti Karttunen, Sep 14 2017

Name corrected by Steven Foster Clark, Sep 05 2023