A192278 - OEIS

%I #6 Mar 30 2012 18:53:49

%S 6,36,96,120,156,216,300,516,576,660,744,804,936,1044,1056,1296,1344,

%T 1356,1500,1560,1584,1680,1764,1836,1884,2064,2136,2400,2484,2616,

%U 2640,2760,2820,2940,3180,3276,3396,3480,3564,3744,3780,4044,4116,4500,4620,4716

%N Numbers n whose product of their anti-divisors divides the product of their divisors.

%C All numbers are even and divisible by 6.

%e n=1884 has the anti-divisors 8, 24, 1256 whose product is 241152 and the divisors 1, 2, 3, 4, 6, 12, 157, 314, 942, 1884, 628, 471 whose product is 44718310871557410816.  Their ratio 44718310871557410816 / 241152 = 185436201530808 is integral so 1884 is a term of the sequence.

%p with(numtheory);

%p P:=proc(i)

%p local a,b,d,k,n;

%p for n from 3 by 1 to i do

%p   a:=1;

%p   for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a*k; fi; od;

%p   d:=divisors(n); b:=1;

%p   for k from 1 to nops(d) do b:=b*d[k]; od;

%p   if trunc(b/a)=b/a then print(n); fi;

%p od;

%p end:

%p P(1000);

%Y Cf. A066272.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Jul 07 2011