PARI's commands

[science_man_88]

they both work until M(1) but after that they climb to 35 and 70 for the next ones.

[science_man_88]

Originally Posted by CRGreathouse

I can't correct the program because I don't know what it's trying to do. But certainly the program isn't doing what you intend if it stores the value it returns but doesn't actually return a value.

it's doing the equivalent of the formula I gave above.

http://www.mersenneforum.org/cgi-bin...1}M(n)%20+%20x

[CRGreathouse]

Is x in the sum or out of the sum?

[science_man_88]

Originally Posted by CRGreathouse

Is x in the sum or out of the sum?

out I know I wasn't sure how to make it obvious. sum all M(n) less than M(x) then add x to that sum.

I realize it should of been first now lol.

[CRGreathouse]

Originally Posted by science_man_88

out I know I wasn't sure how to make it obvious.

would be the usual way. Of course you could also use parentheses (in which case, in LaTeX, you would want to use \left and \right).

M(x)=x+sum(n=0,x-1,M(n))

is the literal translation into Pari.

Here's a solution with memoization. It stores the values rather than recalculating:

M(x)={
  if(x < 1, return(0));
  if(Mvec == 'Mvec,Mvec=[]);
  if(#Mvec < x,
    my(n=#Mvec);
    Mvec=vector(x,i,if(i<=n,Mvec[i]));
    for(i=n+1,x, Mvec[i]=i+sum(j=1,i-1,Mvec[j]))
  );
  Mvec[x]
};

Here's a more efficient version:

M(x)=(1<<x)-1

[science_man_88]

Originally Posted by CRGreathouse

would be the usual way. Of course you could also use parentheses (in which case, in LaTeX, you would want to use \left and \right).

M(x)=x+sum(n=0,x-1,M(n))

is the literal translation into Pari.

Here's a solution with memoization. It stores the values rather than recalculating:

M(x)={
  if(x < 1, return(0));
  if(Mvec == 'Mvec,Mvec=[]);
  if(#Mvec < x,
    my(n=#Mvec);
    Mvec=vector(x,i,if(i<=n,Mvec[i]));
    for(i=n+1,x, Mvec[i]=i+sum(j=1,i-1,Mvec[j]))
  );
  Mvec[x]
};

Here's a more efficient version:

M(x)=(1<<x)-1

memorization* and memorize* for the last few posts but thank's and I have proved it works yeah. is there a formula for the number list that contains the super-perfect numbers and perfect numbers as well like mine ?

[CRGreathouse]

Originally Posted by science_man_88

memorization* and memorize*

No, memoization and memoize. Different words.

Originally Posted by science_man_88

is there a formula for the number list that contains the super-perfect numbers and perfect numbers as well like mine ?

Not sure what you mean.

[science_man_88]

is there a similar formula for the sequences that hold super-perfect and perfect numbers respectively?

[CRGreathouse]

Originally Posted by science_man_88

is there a similar formula for the sequences that hold super-perfect and perfect numbers respectively?

Yes, but what sequences? Certainly they're in A000027, but did you have a more specific sequence in mind? I don't know of an explicit formula for the (super-)perfect numbers, of course -- though I wouldn't be surprised if one could be formed with sin and floor.

[axn]

Originally Posted by science_man_88

memorization* and memorize* for the last few posts

http://en.wikipedia.org/wiki/Memoization

[CRGreathouse]

Originally Posted by axn

http://en.wikipedia.org/wiki/Memoization

Thanks, axn. I tend to forget that not everyone is a computer programmer.