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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).
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%I #18 Feb 10 2017 21:20:02

%S 21,33,63,99,147,189,231,273,297,357,363,399,429,441,483,561,567,609,

%T 627,651,663,693,741,759,777,819,861,891,897,903,957,969,987,1023,

%U 1029,1071,1089,1113,1131,1173,1197,1209,1221,1239,1281,1287,1311,1323,1353,1407,1419,1443,1449

%N 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 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 Subset of A280877.

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

%H A.H.M. Smeets, <a href="/A280878/b280878.txt">Table of n, a(n) for n = 1..11142</a>

%o (Python)

%o from fractions import gcd

%o t = 1

%o to = 1

%o i = 1

%o x = 1

%o while x > 0:

%o ....x = x + 1

%o ....y = 0

%o ....while y < x:

%o ........y = y + 1

%o ........if gcd(x,y) == 1:

%o ............t = t + 2

%o ....e = t*(x-1)*(x-1) - to*x*x

%o ....if (e < 0 and x%2 == 1 and x%6 == 3 and x%30 != 15):

%o ........print(i,x)

%o ........i = i + 1

%o ....to = t

%K nonn

%O 1,1

%A _A.H.M. Smeets_, Jan 09 2017