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%I #32 Jan 25 2021 03:15:17
%S 4,16,36,144,256,576,900,1764,2304,2500,3600,4356,6084,7056,8100,
%T 10000,10404,12996,17424,19044,22500,24336,26244,30276,32400,34596,
%U 36864,41616,49284,51984,57600,60516,65536,66564,76176,79524,90000
%N 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.
%C All members are even squares (A016742). Intersection of A049439 and A181794.
%C Includes all numbers of the form A001146(m)*A036896(n) for m>1.
%H Amiram Eldar, <a href="/A181795/b181795.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..96 from Harvey P. Dale)
%e 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.
%t 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 *)
%o (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
%Y Subsequence of A000290, A016742, A120351.
%Y See also A033950,A181687. For refactorable members of this sequence, see A120349.
%K nonn
%O 1,1
%A _Matthew Vandermast_, Nov 14 2010
%E More terms from _Nathaniel Johnston_, Nov 17 2010
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