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

1,1

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.

Links

Table of n, a(n) for n=1..40.

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

Cf. A005100, A064116.

Sequence in context: A370411 A033395 A143754 * A023146 A031945 A049355

Adjacent sequences: A357037 A357038 A357039 * A357041 A357042 A357043

Keyword

nonn

Author

Tanya Khovanova, Sep 09 2022

Status

approved