new sequences related to partitions

[N. J. A. Sloane]

Dear Seqfans,

Last week Amarnath Murthy proposed some possibly new
sequences, which I think are quite interesting.
Here they are, in case anyone would like to work
with him:

 From amarnath_murthy at yahoo.com  Mon Jun 16 09:04:27 2003

Dear Dr. Sloane,
 I have some  sequence ideas which would be difficult
for me get terms.If  you  find them  worth/interesting
then some one can submit them.

1-A. Let a,b,c,...k be an arbitrary partition of n. 
let ftau(n) = tau(a) +tau(b)+...tau(k).
a(n) = maximum value of ftau(n).

1-B
a(n) = minimum value of ftau(n).
 If n can be partioned into all primes and a 1 then
that would give the minimum ftau(n).

2. Similarly sq(n) can be defined as a^2 +b^2 ...
+k^2. and a(n) =  maximum sq(n).

3. fsigma(n) = sigma(a) + sigma(b) +...+ sigma(k).
a(n) = maximum value of fsigma(n).
More such functions can be defined. And the same can
be extended for  the minimum values.

thanks
regards
amarnath


NJAS