Browsing among the lines in the book of
N.J.Sloane ( Mathematics Research Center Bell Telephone Laboratories.Inc.Murray Hill,New Jersey)
entitled:
"A Handbook of Integer Sequences" (Academic Press, New York and London,1973)
I found
on page 50, under Nr.248. the Mersenne primes (on account of editorial aspects beginning with the number "1"), and
on page 68. under Nr.536. another sequence, namely " Partitions into parts of 2 kinds"
with two references i.e.
- R52 = Royal Society Math. Tables Vol.4.Tables of partitions by Gupta and others .Cambridge Univ. Press, London and New York,1958, 90,
and
-RCI = Riordan: Combinatorial Identities, Wiley, New York 1958, 199
( The first 38 elements of the ulterior sequence are:
1,2,5,10,20,36,65,110,185,300,481,752,1165,1770,2665,3956,5822,8470,12230,17490,24842,35002,
49010,68150,94235,129512,177087,240840,326015,439190,589128,786814,1046705,1386930,
1831065,2408658,3157789,4126070.)
If we count the correlation coefficient of these first
38 elements of the sequences (the 37 known Mersenne primes and the number
"1", and the quoted partition function)
the result would be over 0,96953 with an F-test = 0,9441.
If we count again with only 37 - 37 integer (omitting the beginner
number "1")
the result would be over 0,96952 with an F-test = 0,9391
These results seem to be surprisingly high, even if we are aware of the relation between the sum of divisors and the partition function dealt by Combinatorial Analysis (Partition Theory). However it might be merely a coincidence, the sequences only ran across each other?
Best regards
La'ng Pa'l
(Paul La'ng)
Budapest, Hungary
PS.: As I am also anxious to get knowledge of the 38th amd the 39th Mersenne prime and then to see the distances, and the modified correlation coefficient, I quote also the next ten elements of the mentioned partition sequence, as follows:
5374390, 6978730,9035539,11664896,15018300,19283830,24697480,31551450,40210481,51124970
Regards
La'ngPa'l
