

A357040


Deficient composite numbers whose sum of aliquot divisors as well as product of aliquot divisors is a perfect square.


0



75, 76, 124, 147, 153, 243, 332, 363, 477, 507, 524, 575, 688, 867, 892, 963, 1075, 1083, 1421, 1532, 1573, 1587, 1611, 1916, 2032, 2075, 2224, 2299, 2401, 2421, 2523, 2572, 2883, 2891, 3479, 4107, 4336, 4527, 4961, 4975
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OFFSET

1,1


COMMENTS

Prime numbers are excluded from this sequence as they make a trivial case: they have the sum as well as the product of aliquot divisor equal to 1.


LINKS



EXAMPLE

Aliquot divisors of 75 are 1, 3, 5, 15, and 25. The sum is 49 = 7^2, and the product is 5625 = 75^2. Thus, 75 is in this sequence.


MATHEMATICA

Select[Range[2, 5000], IntegerQ[Sqrt[Total[Drop[Divisors[#], 1]]]] && IntegerQ[Sqrt[Times @@ Drop[Divisors[#], 1]]] && ! PrimeQ[#] && Total[Drop[Divisors[#], 1]] < # &]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



