OFFSET
1,2
COMMENTS
Invented by the HR concept formation program.
Sequence consists of all numbers of the form A000079(k)*A036896(m). - Matthew Vandermast, Nov 14 2010
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Simon Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2 (1999), Article 99.1.2.
Simon Colton, HR - Automatic Theory Formation in Pure Mathematics.
FORMULA
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-François 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 *)
Select[Range[6000], OddQ[(d = DivisorSigma[0, #/2^IntegerExponent[#, 2]])] && Divisible[#, d] &] (* Amiram Eldar, Jun 12 2022 *)
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
KEYWORD
nice,nonn
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
EXTENSIONS
Example corrected by Harvey P. Dale, Jul 14 2011
STATUS
approved