

A120351


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


1



4, 6, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 34, 36, 38, 44, 46, 48, 52, 58, 62, 68, 72, 74, 76, 80, 82, 86, 90, 92, 94, 106, 112, 116, 118, 120, 122, 124, 126, 134, 142, 144, 146, 148, 150, 158, 160, 164, 166, 168, 172, 176, 178, 180, 188, 192, 194, 198, 202, 206
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OFFSET

1,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..60.


FORMULA

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


EXAMPLE

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


MAPLE

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;


CROSSREFS

Cf. A033950, A049439, A057265.
Sequence in context: A287342 A309177 A163164 * A137230 A283564 A181794
Adjacent sequences: A120348 A120349 A120350 * A120352 A120353 A120354


KEYWORD

nonn


AUTHOR

Walter Kehowski, Jun 24 2006


STATUS

approved



