OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
117 is in the sequence because the divisors of 117 are 1, 3, 9, 13, 39 and 117. Being squarefree itself, the product of divisors is a perfect square. The sum of the divisors in question, 3+9+13+39 = 64 and it is a perfect square.
MATHEMATICA
Select[ Range[2, 25000], IntegerQ[ Sqrt[ Apply[ Plus, Delete[ Divisors[ # ], -1]] - 1]] && IntegerQ[ Sqrt[ Apply[ Times, Delete[ Divisors[ # ], -1]]]] && ! PrimeQ[ # ] & ]
aQ[n_] := CompositeQ[n] && IntegerQ[Sqrt[n^(DivisorSigma[0, n]/2 - 1)]] && IntegerQ[Sqrt[DivisorSigma[1, n] - 1 - n]]; Select[Range[18000], aQ] (* Amiram Eldar, Jul 03 2019 *)
PROG
(Magma) [k:k in [1..18000]| not IsPrime(k) and IsSquare((&+Divisors(k))-1-k) and IsSquare((&*Divisors(k))/k) ]; // Marius A. Burtea, Jul 03 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Oct 14 2001
STATUS
approved