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A181795 Numbers n such that the number of odd divisors of n is an odd divisor of n, and the number of even divisors of n is an even divisor of n. 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 (list; graph; refs; listen; history; text; internal format)
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

Harvey P. Dale, Table of n, a(n) for n = 1..96

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)=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

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Last modified November 17 10:07 EST 2018. Contains 317275 sequences. (Running on oeis4.)