

A252233


Characteristic function for the integers that are the product of an odd number of primes each with multiplicity one.


1



0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
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OFFSET

1


COMMENTS

This sequence is the characteristic function for the integers in A030059.
The cumulative sums of the sequence at a(10^k) for k = 1, 2, ..., 6 are 4, 30, 303, 3053, 30421, 303857.


REFERENCES

P. J. McCarthy, Introduction to Arithmetical Functions, Springer Verlag, 1986, page 227, Exercise 5.9.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for characteristic functions
Index entries for sequences computed from exponents in factorization of n


FORMULA

Dirichlet g.f.: (zeta(s)/zeta(2*s)  1/zeta(s))/2
a(n) = (A008966(n)  A008683(n))/2.
a(n) = 1 if n is of the form p_1*p_2*...*p_r for some odd number r, otherwise a(n) = 0.


EXAMPLE

a(4) = 0 because 4 = 2^2 (the prime factors of n must not have exponents other than 1).
a(30) = 1 because 30 = 2*3*5 (there are an odd number of prime factors).


MATHEMATICA

Table[(Abs[MoebiusMu[n]]  MoebiusMu[n])/2, {n, 1, 100}]


PROG

(PARI) A252233(n) = ((issquarefree(n)moebius(n))/2); \\ Antti Karttunen, Oct 08 2017


CROSSREFS

Cf. A092248, A030059, A008966, A008683.
Sequence in context: A227625 A129950 A010051 * A283991 A327861 A131929
Adjacent sequences: A252230 A252231 A252232 * A252234 A252235 A252236


KEYWORD

nonn


AUTHOR

Geoffrey Critzer, Mar 21 2015


STATUS

approved



