# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a049439 Showing 1-1 of 1 %I A049439 #45 Jun 12 2022 02:58:56 %S A049439 1,2,4,8,9,16,18,32,36,64,72,128,144,225,256,288,441,450,512,576,625, %T A049439 882,900,1024,1089,1152,1250,1521,1764,1800,2025,2048,2178,2304,2500, %U A049439 2601,3042,3249,3528,3600,4050,4096,4356,4608,4761,5000,5202,5625,6084 %N A049439 Numbers k such that the number of odd divisors of k is an odd divisor of k. %C A049439 Invented by the HR concept formation program. %C A049439 Sequence consists of all numbers of the form A000079(k)*A036896(m). - _Matthew Vandermast_, Nov 14 2010 %H A049439 Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 %H A049439 Simon Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2 (1999), Article 99.1.2. %H A049439 Simon Colton, HR - Automatic Theory Formation in Pure Mathematics. %F A049439 a(n) = A000079(k)*A016754(m) for appropriate k, m. - _Reinhard Zumkeller_, Jun 05 2008 %e A049439 There are 3 odd divisors of 18, namely 1,3 and 9 and 3 itself is an odd divisor of 18. %t A049439 ok[n_] := (d = Length @ Select[Divisors[n], OddQ] ; %t A049439 IntegerQ[n/d] && OddQ[d]); Select[Range[6100], ok] %t A049439 (* _Jean-François Alcover_, Apr 22 2011 *) %t A049439 odQ[n_]:=Module[{ods=Select[Divisors[n],OddQ]},MemberQ[ods,Length[ ods]]]; Select[Range[7000],odQ] (* _Harvey P. Dale_, Dec 18 2011 *) %t A049439 Select[Range[6000], OddQ[(d = DivisorSigma[0, #/2^IntegerExponent[#, 2]])] && Divisible[#, d] &] (* _Amiram Eldar_, Jun 12 2022 *) %o A049439 (Haskell) %o A049439 a049439 n = a049439_list !! (n-1) %o A049439 a049439_list = filter (\x -> ((length $ oddDivs x) `elem` oddDivs x)) [1..] %o A049439 where oddDivs n = [d | d <- [1,3..n], mod n d == 0] %o A049439 -- _Reinhard Zumkeller_, Aug 17 2011 %o A049439 (PARI) is(n)=my(d=numdiv(n>>valuation(n,2))); d%2 && n%d==0 \\ _Charles R Greathouse IV_, Feb 07 2017 %Y A049439 Contains A000079 and A036896. %Y A049439 Cf. A001227, A033950. %Y A049439 Subsequence of A028982. Includes A120349, A120358, A120359, A120361, A181795. See also A181794. %K A049439 nice,nonn %O A049439 1,2 %A A049439 Simon Colton (simonco(AT)cs.york.ac.uk) %E A049439 Example corrected by _Harvey P. Dale_, Jul 14 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE