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A049439
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Numbers n such that the number of odd divisors of n is an odd divisor of n.
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12
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1, 2, 4, 8, 9, 16, 18, 32, 36, 64, 72, 128, 144, 225, 256, 288, 441, 450, 512, 576, 625, 882, 900, 1024, 1089, 1152, 1250, 1521, 1764, 1800, 2025, 2048, 2178, 2304, 2500, 2601, 3042, 3249, 3528, 3600, 4050, 4096, 4356, 4608, 4761, 5000, 5202, 5625, 6084
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Invented by the HR concept formation program.
a(n) = A000079(k)*A016754(m) for appropriate k, m. - Reinhard Zumkeller, Jun 05 2008
Sequence consists of all numbers of the form A000079(k)*A036896(m). - Matthew Vandermast, Nov 14 2010
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..1000
S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
S. Colton, HR - Automatic Theory Formation in Pure Mathematics
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EXAMPLE
| There are 3 odd divisors of 18, namely 1,3 and 9 and 3 itself is an odd divisor of 18.
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MATHEMATICA
| ok[n_] := (d = Length @ Select[Divisors[n], OddQ] ;
IntegerQ[n/d] && OddQ[d]); Select[Range[6100], ok]
(* From Jean-François Alcover, Apr 22 2011 *)
odQ[n_]:=Module[{ods=Select[Divisors[n], OddQ]}, MemberQ[ods, Length[ ods]]]; Select[Range[7000], odQ] (* From Harvey P. Dale, Dec 18 2011 *)
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PROG
| (Haskell)
a049439 n = a049439_list !! (n-1)
a049439_list = filter (\x -> ((length $ oddDivs x) `elem` oddDivs x)) [1..]
where oddDivs n = [d | d <- [1, 3..n], mod n d == 0]
-- Reinhard Zumkeller, Aug 17 2011
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CROSSREFS
| Contains A000079 and A036896. Cf. A033950.
Subsequence of A028982. Includes A120349, A120358, A120359, A120361, A181795. See also A181794.
Sequence in context: A080025 A152111 A025611 * A079931 A188915 A055008
Adjacent sequences: A049436 A049437 A049438 * A049440 A049441 A049442
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KEYWORD
| nice,nonn
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AUTHOR
| Simon Colton (simonco(AT)cs.york.ac.uk)
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EXTENSIONS
| Example corrected by Harvey P. Dale, Jul 14 2011
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