A120349 Refactorable numbers k such that the number of odd divisors r is odd, the number of even divisors s is even and both r and s are divisors of k.

36, 3600, 8100, 10000, 22500, 26244, 32400, 90000, 142884, 202500, 396900, 518400, 656100, 810000, 980100, 1285956, 1368900, 1587600, 1679616, 2286144, 2340900, 2624400, 2924100

Offset

1,1

Comments

In general, since n is even, r is always a multiple of s and even if both r and s are divisors of n, the sum t=r+s may not be. For example, if n=144, then r=3, s=12 and t=r+s=15.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = n-th number such that n is even, r = number of odd divisors of n, s = number of even divisors of n, t = r+s = number of divisors of n, are all divisors of n and r is odd, s is even.

Example

a(1)=36 since r=3(odd), s=6(even) and t=r+s=9 are all divisors.

Maple

with(numtheory); T := proc(n::posint) local x, y, S; S:=divisors(n); x:=nops( select(z->type(z, odd), S) ); y:=nops( select(z->type(z, even), S) ); return [x, y] end; RF:=[]: N:=12^6/2: CNT:=12^4: for w to 1 do for k from 1 to N do n:=2*k; if k mod CNT = 0 then print((N-k)/CNT) fi; r:=T(n)[1]; s:=T(n)[2]; t:=r+s; if type(s, even) and type(r, odd) and andmap(z -> n mod z = 0, [r, s, t]) then RF:=[op(RF), n]; print(n, r, s, t); fi; od od; RF;

Crossrefs

Cf. A033950, A049439, A057265.

Sequence in context: A072377 A364175 A209267 * A120359 A194611 A165984

Adjacent sequences: A120346 A120347 A120348 * A120350 A120351 A120352

Keyword

nonn

Author

Walter Kehowski, Jun 24 2006

Status

approved