cp's OEIS Frontend

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).

%I A280878 #24 Jun 28 2025 12:55:42
%S A280878 21,33,63,99,147,189,231,273,297,357,363,399,429,441,483,561,567,609,
%T A280878 627,651,663,693,741,759,777,819,861,891,897,903,957,969,987,1023,
%U A280878 1029,1071,1089,1113,1131,1173,1197,1209,1221,1239,1281,1287,1311,1323,1353,1407,1419,1443,1449
%N 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).
%C A280878 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).
%C A280878 Subset of A280877.
%C A280878 Related to Euler phi function A000010 by P(n) = ((2*Sum_{m=1..a(n)} phi(m))-1)/a(n)^2.
%H A280878 A.H.M. Smeets, <a href="/A280878/b280878.txt">Table of n, a(n) for n = 1..11142</a>
%o A280878 (Python)
%o A280878 from math import gcd
%o A280878 t = 1
%o A280878 to = 1
%o A280878 i = 1
%o A280878 x = 1
%o A280878 while x < 1450:
%o A280878     x = x + 1
%o A280878     y = 0
%o A280878     while y < x:
%o A280878         y = y + 1
%o A280878         if gcd(x,y) == 1:
%o A280878             t = t + 2
%o A280878     e = t*(x-1)*(x-1) - to*x*x
%o A280878     if (e < 0 and x%2 == 1 and x%6 == 3 and x%30 != 15):
%o A280878         print(i,x)
%o A280878         i = i + 1
%o A280878     to = t
%K A280878 nonn
%O A280878 1,1
%A A280878 _A.H.M. Smeets_, Jan 09 2017