%I A064180
%S A064180 117,208,292,320,475,539,549,567,873,964,1737,2107,2692,2997,3573,3904,
%T A064180 4477,4802,5275,5284,5968,6057,7267,7488,7492,9189,9457,9475,10084,
%U A064180 10377,11072,11728,11737,12717,13769,14373,14692,16219,16399,17397
%N A064180 The sum of the proper divisors of n not including 1, Chowla'a function 
               (A048050) and the product of the proper divisors or aliquot parts 
               of n (A007956) are both perfect squares.
%e A064180 117 is in the sequence because the divisors of 117 are 1, 3, 9, 13, 39 
               and 117. Being square-free 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.
%t A064180 Select[ Range[2, 25000], IntegerQ[ Sqrt[ Apply[ Plus, Delete[ Divisors[ 
               # ], -1]] - 1]] && IntegerQ[ Sqrt[ Apply[ Times, Delete[ Divisors[ 
               # ], -1]]]] && ! PrimeQ[ # ] & ]
%Y A064180 Sequence in context: A095625 A109023 A112877 this_sequence A050245 A031174 
               A146172
%Y A064180 Adjacent sequences: A064177 A064178 A064179 this_sequence A064181 A064182 
               A064183
%K A064180 easy,nonn
%O A064180 1,1
%A A064180 Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 14 2001