[seqfan] distribution of totatives of a Primorial

[Jamie Morken]

Hi Seqfans,
An algorithm for calculating the number of totatives in an specified range,also showing that totatives of a Primorial can be partitioned into sectionswhich contain equal numbers of totatives.
For Primorial number 2*3*5*7=210, which has 48 totatives, The specified ranges are given by 48/210. 48/210 as a reduced fraction = 8/35.  Creating a set of GCD(210,48) = 6 fractions by adding 8 and 35 respectively to the numerator and denominator of the reduced fraction 8/35 gives:
8/35, 16/70, 24/105, 32/140, 40/175, 48/210. Finding the totatives of 210 which are smaller and nearest to each ofthe denominators: 35,70,105,140,175,210. gives the totatives: 31,67,103,139,173,209. 
Checking the remaining 48-6 = 42 totatives,there are 7 totatives in 6 ranges separated by thetotatives 31,67,103,139,173,209.(1,11,13,17,19,23,29), 
(37,41,43,47,53,59,61), 
(71,73,79,83,89,97,101), 
(107,109,113,121,127,131,137), (143,149,151,157,163,167,169), (179,181,187,191,193,197,199).
The formula to calculate 7 is (48-6)/6=7.where 48 is the number of totatives of Primorial number 210 = 48. and the GCD of 210 and 48 = 6.
Related OEIS sequences:https://oeis.org/A058250https://oeis.org/A038110https://oeis.org/A038111
cheers,Jamie