A Ruth–Aaron pair consists of two consecutive integers (e.g., 714 and 715) for which the sums of the prime divisors of each integer are equal. So called because 714 is Babe Ruth's lifetime home run record; Hank Aaron's 715th home run broke this record and 714 and 715 have the same prime divisor sum.



A Ruth–Aaron triple consists of three consecutive integers with the same properties.



There is a second variant of Ruth–Aaron numbers, one which uses prime factors rather than prime divisors. The difference; divisors are unique, factors may be repeated. The 714, 715 pair appears in both, so the name still fits.



It is common to refer to each Ruth–Aaron group by the first number in it.



Task
 Find and show, here on this page, the first 30 Ruth-Aaron numbers (factors).
 Find and show, here on this page, the first 30 Ruth-Aaron numbers (divisors).


Stretch
 Find and show the first Ruth-Aaron triple (factors).
 Find and show the first Ruth-Aaron triple (divisors).


See also
Wikipedia: Ruth–Aaron pair
OEIS:A006145 - Ruth-Aaron numbers (1): sum of prime divisors of n = sum of prime divisors of n+1
OEIS:A039752 - Ruth-Aaron numbers (2): sum of prime divisors of n = sum of prime divisors of n+1 (both taken with multiplicity)
   NB. using factors
   30{.1 2+/~I. 2 =/\ +/@q: 1+i.100000
    5     6
    8     9
   15    16
   77    78
  125   126
  714   715
  948   949
 1330  1331
 1520  1521
 1862  1863
 2491  2492
 3248  3249
 4185  4186
 4191  4192
 5405  5406
 5560  5561
 5959  5960
 6867  6868
 8280  8281
 8463  8464
10647 10648
12351 12352
14587 14588
16932 16933
17080 17081
18490 18491
20450 20451
24895 24896
26642 26643
26649 26650
 
   NB. using divisors
   30{.1 2+/~I. 2 =/\ (+/@{.@q:~&__) 1+i.100000
    5     6
   24    25
   49    50
   77    78
  104   105
  153   154
  369   370
  492   493
  714   715
 1682  1683
 2107  2108
 2299  2300
 2600  2601
 2783  2784
 5405  5406
 6556  6557
 6811  6812
 8855  8856
 9800  9801
12726 12727
13775 13776
18655 18656
21183 21184
24024 24025
24432 24433
24880 24881
25839 25840
26642 26643
35456 35457
40081 40082