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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 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: A220472 A033395 A143754 * A023146 A031945 A049355 Adjacent sequences: A357037 A357038 A357039 * A357041 A357042 A357043 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.)