

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.


5



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
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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



