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A227291 Characteristic function of squarefree numbers squared (A062503). 6
1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = A008966(A037213(n)), when assumed A008966(0) = 0. - Reinhard Zumkeller, Jul 07 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

FORMULA

Dirichlet g.f.: zeta(2s)/zeta(4s) = prod[prime p: 1+p^(-2s) ], see A008966.

a(n) = A063524(sum(A225817(n,k)*A225817(n,A000005(n)+1-k): k=1..A000005(n))). - Reinhard Zumkeller, Aug 01 2013

Multiplicative with a(p^e) = 1 if e=2, a(p^e) = 0 if e=1 or e>2. - Antti Karttunen, Jul 28 2017

Sum_{k=1..n} a(k) ~ 6*sqrt(n) / Pi^2. - Vaclav Kotesovec, Feb 02 2019

a(n) = A225569(A225546(n)-1). - Peter Munn, Oct 31 2019

EXAMPLE

a(3) = 0 because 3 is not the square of a squarefree number.

a(4) = 1 because sqrt(4) = 2, a squarefree number.

MATHEMATICA

Table[Abs[Sum[MoebiusMu[n/d], {d, Select[Divisors[n], SquareFreeQ[#] &]}]], {n, 1, 200}] (* Geoffrey Critzer, Mar 18 2015 *)

PROG

(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1+X^2)[n])

(Haskell)

a227291 n = fromEnum $ (sum $ zipWith (*) mds (reverse mds)) == 1

   where mds = a225817_row n

-- Reinhard Zumkeller, Jul 30 2013, Jul 07 2013

(Scheme) (define (A227291 n) (if (= 1 n) n (* (if (= 2 (A067029 n)) 1 0) (A227291 (A028234 n))))) ;; Antti Karttunen, Jul 28 2017

CROSSREFS

Cf. A225817, A008683, A027750, A225546, A225569.

Absolute values of A271102.

Sequence in context: A015179 A014504 A014999 * A271102 A326072 A304362

Adjacent sequences:  A227288 A227289 A227290 * A227292 A227293 A227294

KEYWORD

nonn,mult,easy

AUTHOR

Ralf Stephan, Jul 05 2013

STATUS

approved

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Last modified November 29 17:53 EST 2020. Contains 338769 sequences. (Running on oeis4.)