A072301 - OEIS

%I #9 Jun 01 2024 22:06:47

%S 1,2,2,4,2,2,4,5,9,3,4,5,6,5,5,16,6,11,8,6,11,7,8,7,25,8,11,12,8,10,

%T 16,19,11,11,12,29,18,10,17,10,12,14,20,13,14,15,16,23,31,33,17,22,18,

%U 15,19,15,23,15,16,17,30,21,30,64,19,22,32,20,23,23,24,35,36,24,37,26,26

%N Number of positive integers not exceeding n that are relatively prime to sigma(n).

%F a(n) = Sum_{d|sigma(n)} moebius(d)*floor(n/d). - _Ridouane Oudra_, May 12 2024

%e Among the positive integers not exceeding 12, the five numbers 1,3,5,9,11 are relatively prime to sigma(12)=28. Hence a(12)=5.

%p with(numtheory) : seq(add(mobius(d)*floor(n/d), d in divisors(sigma(n))) , n=1..100) ; # _Ridouane Oudra_, May 12 2024

%t r = {}; Do[ s = DivisorSigma[1, n]; j = 0; For[i = 1, i <= n, i++, If[GCD[s, i] == 1, j++ ]]; r = Append[r, j], {n, 1, 10^2}]; r

%Y Cf. A000203.

%K base,nonn

%O 1,2

%A _Joseph L. Pe_, Jul 14 2002