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

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)