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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A220472 A033395 A143754 * A023146 A031945 A049355
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Sep 09 2022
STATUS
approved

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Last modified March 2 12:34 EST 2024. Contains 370467 sequences. (Running on oeis4.)