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A069513 Characteristic function of the prime powers p^k, k >= 1. +0
2
0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 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, 1, 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 (list; graph; listen)
OFFSET

1,1

COMMENT

Also, number of Galois fields of order n. - Charles R Greathouse IV, Mar 12 2008

If n>=2, a(n)=A010055(n).

LINKS

Daniel Forgues, Table of n, a(n) for n=1,...,100000.

Charles R Greathouse IV, Home Page [in lieu of email address]

FORMULA

a(n) = Sum(d divides n,bigomega(d)*mu(n/d)); equivalently, Sum(d divides n,a(d)) = bigomega(n); equivalently, Moebius transform of bigomega(n).

Dirichlet generating function: ppzeta(s). Here ppzeta(s) = sum(p prime, sum(k >= 1, 1/(p^k)^s)). Note that ppzeta(s) = sum(p prime, 1/(p^s-1)) = sum(k >= 1, primezeta(k*s)). - Franklin T. Adams-Watters, Sep 11 2005.

PROGRAM

(PARI) for(n=1, 120, print1(omega(n)==1, ", "))

CROSSREFS

Cf. A010055, A001222, A008683.

The partial sums of this sequence give A025528. [From Daniel Forgues (squid(AT)zensearch.com), Mar 02 2009]

Sequence in context: A131719 A100656 A053867 this_sequence A092248 A106743 A011558

Adjacent sequences: A069510 A069511 A069512 this_sequence A069514 A069515 A069516

KEYWORD

easy,nonn,new

AUTHOR

Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 15 2002

EXTENSIONS

Moved original definition to formula line. Used comment (that I previously added) as definition. - Daniel Forgues (squid(AT)zensearch.com), Mar 08 2009

Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 02 2009

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Last modified November 25 08:46 EST 2009. Contains 167481 sequences.


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