A174275 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16385

Index entries for characteristic functions

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

Adjacent sequences: A174272 A174273 A174274 * A174276 A174277 A174278

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