possible error in A005835

[Joerg Arndt]

A005835 Pseudoperfect (or semiperfect) numbers: some set of proper
divisors of n sums to n.

said to be the complement of
A005100 Deficient numbers: sigma(n) < 2n.
there add the pari/gp code
 for(n=1,100, if(sigma(n)<2*n, print1(n,", ")))

Now A005835 should be
 ? for(n=1,100, if(sigma(n)>=2*n, print1(n,", ")))

 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72,
 78, 80, 84, 88, 90, 96, 100,

... but 70 is missing in A005835

Should the defn of A005835 be
Pseudoperfect (or semiperfect) numbers: some set of _distinct_ proper
divisors of n sums to n.
(or: not all divisors are allowed to be equal?)



%I A136404
%S A136404 1,4,16,36,144,576,900,3600
%N A136404 Square numbers with more divisors than any smaller square  
number.
%C A136404 Being the square of a number in A002182 is neither  
necessary nor sufficient.
%C A136404 Conjecture: square roots of the terms of this sequence are  
the same terms as A126098
%e A136404 900 qualifies because 576 has only 21 divisors and 900 has  
27. 1296 does not because 1296 has only 25 divisors as opposed to the  
27 of the smaller 900.
%Y A136404 Cf. A002182.
%K A136404 more,nonn,new
%O A136404 1,2
%A A136404 J. Lowell (jhbubby(AT)mindspring.com), Mar 30 2008


Regarding the conjecture: square roots of the terms of this sequence  
are the same terms as A126098...

%I A126098
%S A126098  
1,2,4,6,12,24,30,60,120,180,210,360,420,840,1260,1680,2520,4620,7560,
%T A126098  
9240,13860,18480,27720,55440,83160,110880,120120,180180,240240,360360,
%U A126098  
720720,1081080,1441440,1801800,2042040,2882880,3063060,4084080,5405400,6126120,12252240 
,
%N A126098 Where records occur in A018892.

One of the descriptions for A018892 is "Number of divisors of n^2 less  
than or equal to n."


Now, my attempted proof of the conjecture...

An alternate description for A136404 [square numbers with more  
divisors than any smaller square number] might be: "squares of where  
records occur in A048691." That's because A048691 is the (total)  
number of divisors of n^2.

Now, A048691 = 2*A018892 - 1, so if a record occurs in A018892, it is  
also a record in A048691. Thus A126098 gives not only where records  
occur in A018892, but also where records occur in A048691, and  
therefore, those indices are the square roots of A136404.

Now, if all that makes sense, you can just square the terms of A126098  
to extend A136404.

Hans