OFFSET
1,1
COMMENTS
a(n) = signum(A065332(n)), where signum = A057427. a(n) = if A065330(n) = 1 then 1 else 0 = 1 - signum(A065330(n) - 1).
Dirichlet inverse of b(n) where b(n) = 0 except for: b(1) = b(6) = -b(2) = -b(3) = 1. - Alexander Adam, Dec 26 2012
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
A. Pakapongpun, T. Ward, Functorial Orbit counting, JIS 12 (2009) 09.2.4, example 9.
FORMULA
a(n) = if n = A003586(k) for some k then 1 else 0.
a(n) = Product_{p prime and p|n} 0^floor(p/4). - Reinhard Zumkeller, Nov 19 2004
Multiplicative with a(2^e) = a(3^e) = 1, a(p^e) = 0 for prime p > 3. Dirichlet g.f. 1/(1-2^-s)/(1-3^-s). - Franklin T. Adams-Watters, Sep 01 2006
a(n) = Sum_{d|n} mu(6*d). - Benoit Cloitre, Oct 18 2009
MATHEMATICA
a[n_] := Boole[ 2^IntegerExponent[n, 2] * 3^IntegerExponent[n, 3] == n]; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, May 16 2013, after Charles R Greathouse IV *)
PROG
(PARI) a(n)=sumdiv(n, d, moebius(6*d)) \\ Benoit Cloitre, Oct 18 2009
(PARI) a(n)=3^valuation(n, 3)<<valuation(n, 2)==n \\ Charles R Greathouse IV, Aug 21 2011
(Haskell)
a065333 = fromEnum . (== 1) . a038502 . a000265
-- Reinhard Zumkeller, Jan 08 2013, Apr 12 2012
CROSSREFS
KEYWORD
mult,nonn,easy
AUTHOR
Reinhard Zumkeller, Oct 29 2001
STATUS
approved