A280878 Occurrences of decrease of the probability density P(n) of coprime numbers k,m, satisfying 1 <= k <= a(n) and 1 <= m <= a(n), and a(n) congruent to 1(mod 2) and a(n) congruent to {3,9,21,27}(mod 30).

21, 33, 63, 99, 147, 189, 231, 273, 297, 357, 363, 399, 429, 441, 483, 561, 567, 609, 627, 651, 663, 693, 741, 759, 777, 819, 861, 891, 897, 903, 957, 969, 987, 1023, 1029, 1071, 1089, 1113, 1131, 1173, 1197, 1209, 1221, 1239, 1281, 1287, 1311, 1323, 1353, 1407, 1419, 1443, 1449

Offset: 1

Author

A.H.M. Smeets, Jan 09 2017

Keywords

• nonn

Comments

Probability densities satisfying P(a(n)) < P(a(n)-1) and 1 <= m <= a(n), and a(n) congruent to 1(mod 2) and a(n) congruent to {3,9,21,27}(mod 30).

Subset of A280877.

Related to Euler phi function A000010 by P(n) = ((2*Sum_{m=1..a(n)} phi(m))-1)/a(n)^2.

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..11142

Programs

Python

from math import gcd
t = 1
to = 1
i = 1
x = 1
while x < 1450:
    x = x + 1
    y = 0
    while y < x:
        y = y + 1
        if gcd(x,y) == 1:
            t = t + 2
    e = t*(x-1)*(x-1) - to*x*x
    if (e < 0 and x%2 == 1 and x%6 == 3 and x%30 != 15):
        print(i,x)
        i = i + 1
    to = t