Statistics about the known and unknown gnu's in the range [1,50000]

[gnufinder]

The statistics are based on the currently known gnu's in the range [1,50000]

known gnu's    : 48 991
unknown gnu's  :  1 009

group-deficient numbers (gnu(n)<n) : 48 826
group-perfect numbers   (gnu(n)=n) :      1
group-abundant numbers  (gnu(n)>n) :    164

Number of gnu's with given number of digits :

1  33969
2  10932
3   3184
4    746
5    110
6      2
7     44
8      2
9      1
10     0
11     1

Number of unknown gnu's, such that the lower bound lb(n) has the given number of digits :

1     0
2    12
3   151
4   462
5   200
6    31
7    49
8    42
9    15
10    0
11   46
12    1

largest exponent in the prime factorization of the unknown values :

<=2             0
<=3            27
<=4           231
<=5           471
<=6           726
<=7           856

odd unknown values

[ 10935, 11907, 15309, 16875, 18225, 18711, 19683, 21609, 22113, 24057,
  25515, 27783, 28125, 28431, 30375, 32805, 35721, 36015, 37179, 39375,
  40095, 41067, 41553, 42525, 43659, 43923, 45927, 46305, 46875, 47385, 49005
 ]

single even unknown values ( residue class 2 modulo 4)

[ 4374, 7290, 10206, 11250, 12150, 13122, 14406, 16038, 17010, 18750, 18954,
  20250, 21870, 23814, 24010, 24786, 26250, 26730, 27702, 28350, 29282,
  30618, 31250, 31590, 33534, 33614, 33750, 36450, 37422, 39366, 39546,
  39690, 41250, 41310, 42282, 43218, 43750, 44226, 44550, 45198, 46170,
  47142, 48114, 48438, 48750 ]

[olexandr-konovalov]

@gnufinder nice! what do you mean by "largest exponent in the prime factorization of the unknown values" - I'd expect to see there, for, example, 11 for 2048.

[gnufinder]

For example, 856 of the numbers n in the range [1,50000] , for which gnu(n) is unknown, have no exponent larger than 7 in the prime factorization. I did not complete this table, if you want , I can do it. By the way, the largest exponent occuring is 15 (the number 2^15=32768). Perhaps, you prefer the table below.

[gnufinder]

Number of unknown values with given maximal exponent in the prime factorization :

1     0
2     0
3    27
4   204
5   240
6   255
7   130
8    57
9    49
10   23
11   12
12    6
13    3
14    2
15    1

[olexandr-konovalov]

@gnufinder this is nice! If you have a GAP function that generates this report, please consider submitting it as a pull request. I suggest to have a file lib/stats.g and a function there called GnuStatistics, which accepts a list, in the same way like GnuWishlist does.

With such report generator, we could publish the overview periodically on wiki at https://github.com/alex-konovalov/gnu/wiki (it has already one page where I've collected some bibliography) - that would be a better place for such table than an issue which should be eventually closed...