

A195199


Smallest multiple of n with more than twice as many divisors as n.


2



4, 12, 12, 24, 20, 36, 28, 48, 36, 60, 44, 120, 52, 84, 60, 96, 68, 144, 76, 120, 84, 132, 92, 240, 100, 156, 108, 168, 116, 180, 124, 192, 132, 204, 140, 360, 148, 228, 156, 240, 164, 252, 172, 264, 180, 276, 188, 480, 196, 300, 204, 312, 212, 432, 220, 336
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


LINKS

Table of n, a(n) for n=1..56.


FORMULA

a(n) = min{k*n: A000005(k*n) > 2*A000005(n)}.


EXAMPLE

a(4) must have more than 6 divisors because 4 has 3 divisors and 3*2=6. Therefore, it cannot be 16 because 16 has only 5 divisors.


MAPLE

A195199 := proc(n)
for k from 2 do
if numtheory[tau](k*n) > 2*numtheory[tau](n) then
return k*n ;
end if;
end do:
end proc: # R. J. Mathar, Oct 21 2011


MATHEMATICA

Table[d = DivisorSigma[0, n]; m = 1; While[DivisorSigma[0, m*n] <= 2*d, m++]; m*n, {n, 100}] (* T. D. Noe, Oct 21 2011 *)


CROSSREFS

Sequence in context: A005886 A096442 A211437 * A294628 A323188 A284126
Adjacent sequences: A195196 A195197 A195198 * A195200 A195201 A195202


KEYWORD

nonn


AUTHOR

J. Lowell, Oct 12 2011


STATUS

approved



