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Search: id:A068068
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| A068068 |
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Number of odd unitary divisors of n. d is a unitary divisor of n if d divides n and GCD(d,n/d)=1. |
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+0
8
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Shadow transform of triangular numbers.
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.
Multiplicative with a(2^e) = 1, a(p^e) = 2, p>2. Christian G. Bower (bowerc(AT)usa.net) May 18, 2005.
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
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REFERENCES
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L. J. Gerstein, Pythagorean triples and inner products, Math. Mag., 78 (2005), 205-213. (See Table 1.)
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LINKS
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Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5 (1999) 138-150. (ps, pdf)
N. J. A. Sloane, Transforms
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FORMULA
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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.
a(n)=A024361(4n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 12 2006
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MATHEMATICA
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a[n_] := Length[Select[Divisors[n], OddQ[ # ]&&GCD[ #, n/# ]==1&]]
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CROSSREFS
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Cf. A056901, A068067.
Sequence in context: A043529 A080942 A099812 this_sequence A092505 A066086 A160520
Adjacent sequences: A068065 A068066 A068067 this_sequence A068069 A068070 A068071
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KEYWORD
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nonn,mult
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 19 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jun 08 2002
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