%I
%S 1,18,28,40,84,120,208,372,424,552,624,900,1152,1848,2784,3904,4488,
%T 4992,7448,7896,9120,11712,13720,14280,19920,22344,26040,27144,37920,
%U 41160,52920,88920,107100,132480,186732,195300,208152,240240,243432
%N Numbers k such that sigma(k)  usigma(k) is a square and sets a new record for such squares.
%H Harry J. Smith, <a href="/A063840/b063840.txt">Table of n, a(n) for n = 1..100</a>
%o (PARI) a=1; u(n) = sumdiv(n,d, if(gcd(d,n/d)==1,d)); j=[];
%o for(n=1,300000,x=sigma(n)u(n); if(issquare(x),b=x; if(b>a,a=b; j=concat(j,n)))); j
%o (PARI) u(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
%o { n=0; a=1; for (m=1, 10^9, if(issquare(b=sigma(m)  u(m)), if(b>a, a=b; write("b063840.txt", n++, " ", m); if (n==100, break))) ) } \\ _Harry J. Smith_, Sep 01 2009
%Y Cf. A048146.
%K nonn
%O 1,2
%A _Jason Earls_, Aug 25 2001
