Search: id:A068068
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%I A068068
%S A068068 1,1,2,1,2,2,2,1,2,2,2,2,2,2,4,1,2,2,2,2,4,2,2,2,2,2,2,2,2,4,2,1,4,2,4,
%T A068068 2,2,2,4,2,2,4,2,2,4,2,2,2,2,2,4,2,2,2,4,2,4,2,2,4,2,2,4,1,4,4,2,2,4,4,
%U A068068 2,2,2,2,4,2,4,4,2,2,2,2,2,4,4,2,4,2,2,4,4,2,4,2,4,2,2,2,4,2,2,4,2,2,8
%N A068068 Number of odd unitary divisors of n. d is a unitary divisor of n if d 
               divides n and GCD(d,n/d)=1.
%C A068068 Shadow transform of triangular numbers.
%C A068068 a(n) is the number of primitive Pythagorean triangles with inradius n. 
               For the smallest inradius of exactly 2^n primitive Pythagorean triangles 
               see A070826.
%C A068068 Multiplicative with a(2^e) = 1, a(p^e) = 2, p>2. Christian G. Bower (bowerc(AT)usa.net) 
               May 18, 2005.
%C A068068 Number of primitive Pythagorean triangles with leg 4n. For smallest (even) 
               leg of exactly 2^n PPTs, see A088860. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 12 2006
%D A068068 L. J. Gerstein, Pythagorean triples and inner products, Math. Mag., 78 
               (2005), 205-213. (See Table 1.)
%H A068068 Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects 
               of a combinatorial function, Notes on Number Theory and Discrete 
               Mathematics 5 (1999) 138-150. (<a href="http://math.berkeley.edu/
               ~halbeis/publications/psf/seq.ps">ps</a>, <a href="http://math.berkeley.edu/
               ~halbeis/publications/pdf/seq.pdf">pdf</a>)
%H A068068 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A068068 a(n) = A034444(2n)/2. If n is even, a(n) = 2^(omega(n)-1); if n is odd, 
               a(n) = 2^omega(n). Here omega(n) = A001221(n) is the number of distinct 
               prime divisors of n.
%F A068068 a(n)=A024361(4n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 12 2006
%t A068068 a[n_] := Length[Select[Divisors[n], OddQ[ # ]&&GCD[ #, n/# ]==1&]]
%Y A068068 Cf. A056901, A068067.
%Y A068068 Sequence in context: A043529 A080942 A099812 this_sequence A092505 A066086 
               A160520
%Y A068068 Adjacent sequences: A068065 A068066 A068067 this_sequence A068069 A068070 
               A068071
%K A068068 nonn,mult
%O A068068 1,3
%A A068068 Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 19 2002
%E A068068 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 08 2002

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