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%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
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