A357040 Deficient composite numbers whose sum of aliquot divisors as well as product of aliquot divisors is a perfect square.

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

Offset: 1

Author

Tanya Khovanova, Sep 09 2022

Keywords

• nonn

Comments

Deficient number in A064116; that is, the intersection of A064116 and A005100.

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.

Examples

			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.
		

Crossrefs

Cf. A005100, A064116.

Programs

Mathematica

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