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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. 4
36, 3600, 8100, 10000, 22500, 26244, 32400, 90000, 142884, 202500, 396900, 518400, 656100, 810000, 980100, 1285956, 1368900, 1587600, 1679616, 2286144, 2340900, 2624400, 2924100 (list; graph; refs; listen; history; text; internal format)



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.


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


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.


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


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;


Cf. A033950, A049439, A057265.

Sequence in context: A291911 A072377 A209267 * A120359 A194611 A165984

Adjacent sequences:  A120346 A120347 A120348 * A120350 A120351 A120352




Walter Kehowski, Jun 24 2006



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Last modified June 18 11:58 EDT 2021. Contains 345098 sequences. (Running on oeis4.)