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

1,1

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

Prog

(Python)
from fractions import gcd
t = 1
to = 1
i = 1
x = 1
while x > 0:
....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

Crossrefs

Sequence in context: A233562 A128283 A354837 * A033901 A033656 A270074

Adjacent sequences: A280875 A280876 A280877 * A280879 A280880 A280881

Keyword

nonn

Author

A.H.M. Smeets, Jan 09 2017

Status

approved