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A049439 Numbers n such that the number of odd divisors of n is an odd divisor of n. 12
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; text; internal format)
OFFSET

1,2

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

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

EXAMPLE

There are 3 odd divisors of 18, namely 1,3 and 9 and 3 itself is an odd divisor of 18.

MATHEMATICA

ok[n_] := (d = Length @ Select[Divisors[n], OddQ] ;

  IntegerQ[n/d] && OddQ[d]); Select[Range[6100], ok]

(* Jean-Fran├žois Alcover, Apr 22 2011 *)

odQ[n_]:=Module[{ods=Select[Divisors[n], OddQ]}, MemberQ[ods, Length[ ods]]]; Select[Range[7000], odQ] (* Harvey P. Dale, Dec 18 2011 *)

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

(PARI) is(n)=my(d=numdiv(n>>valuation(n, 2))); d%2 && n%d==0 \\ Charles R Greathouse IV, Feb 07 2017

CROSSREFS

Contains A000079 and A036896.  Cf. A033950.

Subsequence of A028982. Includes A120349, A120358, A120359, A120361, A181795. See also A181794.

Sequence in context: A152111 A316856 A025611 * A251642 A079931 A188915

Adjacent sequences:  A049436 A049437 A049438 * A049440 A049441 A049442

KEYWORD

nice,nonn

AUTHOR

Simon Colton (simonco(AT)cs.york.ac.uk)

EXTENSIONS

Example corrected by Harvey P. Dale, Jul 14 2011

STATUS

approved

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Last modified November 18 01:06 EST 2018. Contains 317279 sequences. (Running on oeis4.)