Sum of prime divisors for Mersenne Numbers?

kurtulmehtap · 2011-01-17, 16:16

I've seen some papers on the sum of prime divisors of any Number.
Are there any papers on sum of prime divisors of Mersenne Numbers?
At least we know that the Sum is equal to
k2q + z where z is the number of prime factors. Do we know anything else?

R.D. Silverman · 2011-01-17, 19:29

Quote:

Originally Posted by kurtulmehtap

I've seen some papers on the sum of prime divisors of any Number.
Are there any papers on sum of prime divisors of Mersenne Numbers?
At least we know that the Sum is equal to
k2q + z where z is the number of prime factors. Do we know anything else?

Not AFAIK.

davar55 · 2011-01-19, 14:59

I did post some puzzles involving sums of Mersenne Prime Exponents
(MPEs) that were worked on by this forum. You might look for those
threads in the Puzzle sub-forum.

science_man_88 · 2011-01-19, 18:48

Quote:

Originally Posted by davar55

I did post some puzzles involving sums of Mersenne Prime Exponents
(MPEs) that were worked on by this forum. You might look for those
threads in the Puzzle sub-forum.

I don't know if that's relevant at this time davar55. The thread here is about sums of the numbers themselves not exponents and not just for primes according to the title. But if you want I'll look for them as I've actually thought about this myself I even had a script in PARI to do some work.

2011-01-17, 16:16	#1
kurtulmehtap Sep 2009 2²×3² Posts	Sum of prime divisors for Mersenne Numbers? I've seen some papers on the sum of prime divisors of any Number. Are there any papers on sum of prime divisors of Mersenne Numbers? At least we know that the Sum is equal to k2q + z where z is the number of prime factors. Do we know anything else?

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2011-01-19, 14:59	#3
davar55 May 2004 New York City 5×7×11² Posts	I did post some puzzles involving sums of Mersenne Prime Exponents (MPEs) that were worked on by this forum. You might look for those threads in the Puzzle sub-forum.