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

1,1

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.

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Subsequence of A000290, A016742, A120351.

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

Sequence in context: A206981 A318149 A233409 * A277285 A136404 A176471

Adjacent sequences: A181792 A181793 A181794 * A181796 A181797 A181798

Keyword

nonn

Author

Matthew Vandermast, Nov 14 2010

Extensions

More terms from Nathaniel Johnston, Nov 17 2010

Status

approved