A181795 Numbers k such that the number of odd divisors of k is an odd divisor of k, and the number of even divisors of k is an even divisor of k.

4, 16, 36, 144, 256, 576, 900, 1764, 2304, 2500, 3600, 4356, 6084, 7056, 8100, 10000, 10404, 12996, 17424, 19044, 22500, 24336, 26244, 30276, 32400, 34596, 36864, 41616, 49284, 51984, 57600, 60516, 65536, 66564, 76176, 79524, 90000

Offset: 1

Author

Matthew Vandermast, Nov 14 2010

Keywords

• nonn

Comments

All members are even squares (A016742). Intersection of A049439 and A181794.

Includes all numbers of the form A001146(m)*A036896(n) for m>1.

Examples

			a(3)=36 has 3 odd divisors (1, 3, and 9) and 6 even divisors (2, 4, 6, 12, 18, and 36). 3 and 6 are odd and even respectively, and both are divisors of 36.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..96 from Harvey P. Dale)

Crossrefs

Subsequence of A000290, A016742, A120351.

See also A033950,A181687. For refactorable members of this sequence, see A120349.

Programs

Mathematica

ndQ[n_]:=Module[{d=Divisors[n],od,ev},od=Count[d,?OddQ];ev=Count[ d, ?EvenQ]; ev!=0&&OddQ[od]&&EvenQ[ev]&&Divisible[n,od]&&Divisible[ n, ev]]; Select[Range[100000],ndQ] (* Harvey P. Dale, Feb 24 2016 *)

PARI

isok(n) = my(nod = numdiv(n>>valuation(n, 2)), noe = if (n%2, 0, numdiv(n/2))); (nod % 2) && nod && !(n % nod) && !(noe % 2) && noe && !(n % noe); \\ Michel Marcus, Jan 14 2014

Extensions

More terms from Nathaniel Johnston, Nov 17 2010