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 A120351 Even numbers such that the number of odd divisors r and the number of even divisors s are both divisors of n. 1

%I

%S 4,6,10,12,14,16,18,20,22,24,26,28,34,36,38,44,46,48,52,58,62,68,72,

%T 74,76,80,82,86,90,92,94,106,112,116,118,120,122,124,126,134,142,144,

%U 146,148,150,158,160,164,166,168,172,176,178,180,188,192,194,198,202,206

%N Even numbers such that the number of odd divisors r and the number of even divisors s are both divisors of n.

%C Since s=0 if n is odd, the number n is necessarily even and then s is always a multiple of r. Note that t=r+s may not be a divisor even if both r and s are divisors. For example, if n=144, then r=3, s=12, but t=r+s=15.

%F a(n) = n is even, r = number of odd divisors of n, s = number of even divisors of n, are all divisors of n.

%e a(2)=16 since r=1 and s=4 are both divisors.

%p with(numtheory); A:=[]: N:=10^4/2: for w to 1 do for k from 2 to N do n:=2*k; S:=divisors(n); r:=nops( select(z->type(z,odd),S) ); s:=nops( select(z->type(z,even),S) ); if andmap(z -> n mod z = 0,[r,s]) then A:=[op(A),n]; print(n,r,s); fi; od od; A;

%Y Cf. A033950, A049439, A057265.

%K nonn

%O 1,1

%A _Walter Kehowski_, Jun 24 2006

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Last modified August 19 08:14 EDT 2019. Contains 326115 sequences. (Running on oeis4.)