A192278 Numbers n whose product of their anti-divisors divides the product of their divisors.

6, 36, 96, 120, 156, 216, 300, 516, 576, 660, 744, 804, 936, 1044, 1056, 1296, 1344, 1356, 1500, 1560, 1584, 1680, 1764, 1836, 1884, 2064, 2136, 2400, 2484, 2616, 2640, 2760, 2820, 2940, 3180, 3276, 3396, 3480, 3564, 3744, 3780, 4044, 4116, 4500, 4620, 4716

Offset

1,1

Comments

All numbers are even and divisible by 6.

Links

Table of n, a(n) for n=1..46.

Example

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.

Maple

with(numtheory);
P:=proc(i)
local a, b, d, k, n;
for n from 3 by 1 to i do
  a:=1;
  for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a*k; fi; od;
  d:=divisors(n); b:=1;
  for k from 1 to nops(d) do b:=b*d[k]; od;
  if trunc(b/a)=b/a then print(n); fi;
od;
end:
P(1000);

Crossrefs

Cf. A066272.

Sequence in context: A108158 A207559 A207414 * A207106 A207306 A207112

Adjacent sequences: A192275 A192276 A192277 * A192279 A192280 A192281

Keyword

nonn

Author

Paolo P. Lava, Jul 07 2011

Status

approved