A064116 -id:A064116 - cp's OEIS frontend

A064121 Nonprime numbers n such that the sum of aliquot divisors of n (A001065) and product of aliquot divisors of n (A048741) are both perfect squares.

1, 12, 75, 76, 124, 147, 153, 176, 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, 3100, 3479, 3776, 3888, 4107, 4336, 4527, 4961, 4975

Offset: 1

Robert G. Wilson v, Oct 14 2001

Amiram Eldar, Table of n, a(n) for n = 1..10000

Variant of A064116. - R. J. Mathar, Oct 02 2008

Cf. A064710.

Select[ Range[5000], IntegerQ[ Sqrt[ Apply[ Plus, Delete[ Divisors[ # ], -1]]]] && IntegerQ[ Sqrt[ Apply[ Times, Delete[Divisors[ # ], -1]]]] && ! PrimeQ[ # ] & ]

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

Original entry on oeis.org

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

Tanya Khovanova, Sep 09 2022

nonn

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.

			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.

Cf. A005100, A064116.

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

cp's OEIS Frontend

A064121 Nonprime numbers n such that the sum of aliquot divisors of n (A001065) and product of aliquot divisors of n (A048741) are both perfect squares.

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