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A212793 Characteristic function of cubefree numbers, A004709. 29
1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

a(A004709(n)) = 1, a(A046099(n)) = 0;

a(n) = abs(A053864(n)).

The following four statements are equivalent: m is cubefree; a(m) = 1; m = A004709(k) for some k; A124010(m,k) <= 2 for all k = 1..A001221(m). - Reinhard Zumkeller, Mar 04 2015

LINKS

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

Eric Weisstein's World of Mathematics, Cubefree

Index entries for characteristic functions

FORMULA

a(n) = A000007(A000005(n) - A073184(n)).

Multiplicative with a(p^e) = 1 if e<=2, =0 if e>=3. - R. J. Mathar, Dec 17 2012

sum(n>0, a(n)/n^s) = product(p prime, 1+p^(-s)+p^(-2s) ) = zeta(s) / zeta(3s). - Ralf Stephan, Jul 07 2013

MATHEMATICA

Table[Boole[Max[FactorInteger[n][[All, 2]]] < 3], {n, 1, 100}] (* Geoffrey Critzer, Feb 25 2015 *)

PROG

(Haskell)

a212793 = cubeFree a000040_list 0 0 where

   cubeFree ps'@(p:ps) q e x

      | e > 2     = 0

      | x == 1    = 1

      | r > 0     = cubeFree ps  p 0 x

      | otherwise = cubeFree ps' p (e + 1) x' where (x', r) = divMod x p

-- Reinhard Zumkeller, Mar 04 2015, May 27 2012

(PARI) a(n) = {f = factor(n); for (i=1, #f~, if ((f[i, 2]) >=3, return(0)); ); return (1); } \\ Michel Marcus, Feb 10 2015

CROSSREFS

Cf. A000005, A000007, A004709, A008966, A046099, A053864, A060431, A124010.

Sequence in context: A305940 A119981 A115789 * A053864 A189021 A307420

Adjacent sequences:  A212790 A212791 A212792 * A212794 A212795 A212796

KEYWORD

nonn,mult

AUTHOR

Reinhard Zumkeller, May 27 2012

STATUS

approved

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Last modified November 17 15:57 EST 2019. Contains 329235 sequences. (Running on oeis4.)